According to Wikipedia France is the most visited country in the world. At the same time, the USA is still practicing the death penalty. For example, 28 people were executed in 2015. For each execution a lot of evidence can be potentially gathered (official documents, video footage, declarations of individuals, etc).
So could the people who have taken part in an execution be considered guilty of "collective murder"? Is it possible that they could be arrested as soon as they arrive in France?
I said this in a comment, but I'll put it in an answer. When France forcibly confines an American, the United States is entitled to ask France, "what the hell do you think you're doing, trying to confine our citizen in your country?" There are really just six basic answers that the United States will accept, and nothing in this scenario is specific to France or the US (it applies any time a foreign national is arrested by any country), and the six responses are the six basic principles of jurisdiction:
Active nationality: "He's our citizen too! What the hell do you think you're doing, questioning how we treat our own citizens?" The US doesn't generally get to question how France treats French citizens, even if they're also American citizens. And France gets to require its citizens to obey French law anywhere in the world.
Subjective territoriality: "He broke our laws on our soil. We don't care that he's your citizen, he has to obey our laws while he's here." This and nationality are by far the most well-accepted answers.
Protective: "He threatened our state. We have the right to protect ourselves." This applies to things like attacking French government personnel or forging a French passport or similar: France isn't protecting its citizens, it's protecting France itself.
Objective territoriality: "He may have committed this crime outside France, but its effects happened inside France. We can punish him for causing those effects." For instance, if you're in the US but hack a computer in France, France has an argument that they get to punish you for that.
Passive nationality: "He may be American and have done this outside France, but he hurt our citizens. We have the right to protect our citizens." Again, a plausible argument. This is not necessarily a strong argument, but it can be made.
Universality: "This thing is a crime against all of humanity. It's something that needs to be stamped out by all countries working together, without worrying too much about whether or not the defendant actually affected the country prosecuting him in any way." This is very rare.
Murder is not a crime of universal jurisdiction. It's limited to more severe crimes, as well as crimes of a fundamentally international nature. So piracy is on the list, as is plane hijacking, as is genocide. Killing an ambassador is on the list: you're a threat to international order. But normal murder? Not even close. It's not a crime with international implications, and it's not a crime which is so fundamentally horrific that it needs to be ended by any means necessary. The death penalty has never been considered to be that fundamentally horrific, and likely never will be, particularly when (as in the US) it is limited to people who have committed something that is an extremely serious crime in any country (i.e. murder).
The only way France could make a remotely plausible argument that it gets to punish American executioners is if they're dual citizens or if they executed a French citizen. Then France can't arrest the executioner because US is a sovereign state and gets to impose its own penal laws. But normally? France couldn't arrest them even if it wasn't for the fact that they're executing US government policy, because Americans in America don't generally have to obey French laws.
In short, it is doubtful that France would arrest an executioner vacationing abroad. The concept of functional immunity relies on mutual respect of sovereigns and applies to government officials acting in their official capacities. From Wikipedia:
Functional immunity arises from customary international law and treaty law and confers immunities on those performing acts of state (usually a foreign official). Any person who in performing an act of state commits a criminal offence is immune from prosecution. This is so even after the person ceases to perform acts of state. Thus it is a type of immunity limited in the acts to which it attaches (acts of state) but will only end if the state itself ceases to exist. This immunity, though applied to the acts of individuals, is an attribute of a state, and is based on the mutual respect of states for sovereign equality and state dignity. States thus have a significant interest in upholding the principle in international affairs: if a state's officials are to be tried at all for anything, it will be at home.
State offices usually recognised as automatically attracting this immunity are the head of state or head of government, senior cabinet members, ambassadors and the foreign and defence ministers. Many countries have embodied these immunities in domestic law. States regularly assert that every official acting in their official capacity is immune from prosecution by foreign authorities (for non-international crimes) under the doctrine of ratione materiae. Such officers are immune from prosecution for everything they do during their time in office. For example, an English court held that a warrant could not be issued for the arrest of Robert Mugabe on charges of international crimes on the basis that he was a presently serving Head of State at the time the proceedings were brought. Other examples are the attempts to prosecute Fidel Castro in Spain and Jiang Zemin in the USA.
You might argue that this doesn't apply to low-level officials like those administering capital punishment but I don't know if that is convincing. Clearly, the US believes they are acting in their official capacities or the US would arrest them.
To arrest an executioner from the US for the crime of carrying out his or her official duty would be to deny the sovereignty of the United States and might be dealt with harshly.
There is one immediate reason why France wouldn't arrest a US executioner; that executioner hasn't committed any crime in France. France doesn't give speeding tickets to people who were speeding in the USA, they don't arrest thieves who steal in the USA, they don't even try murderers who murdered in the USA.
In addition, it is doubtful that an executioner is committing a crime according to French law. In France, you cannot be legally given a death sentence. Therefore the situation cannot arise that in France an executioner kills someone who has been legally condemned to death in France. That doesn't mean executing someone who was legally convicted to a death sentence would be illegal, it just doesn't happen. (It would be different if the death sentence itself had been illegal).
In somewhat related cases, when members of US secret services have abducted people from Europe, that has led to prosecution and convictions, for example in Italy.
Before you get to international law issues, it is uncommon for a state to have a law against murder that applies outside of the state's territory.
For example, in 2003 it was alleged that a US citizen (Tina Watson) was murdered by another US citizen in Australia. In order to try the alleged offender in the United States (specifically in Alabama), the prosecutor had to prove that there was a conspiracy and that part of the conspiracy was carried out in the US. (They were not able to so prove.)
Since 2002, Australia has had a law that says that if you murder an Australian citizen anywhere in the world then you can be tried in Australia: Criminal Code (Cth), s 115.1. This law was enacted in response to a terrorist attack in Indonesia in which many Australians well killed. This law might apply if the US executed an Australian citizen. There is a defence in the Commonwealth Criminal Code for lawful authority (s 10.5) but the word "law" is defined in the Code's Dictionary to refer to Commonwealth law, not foreign law.
The Australian authorities would then look at the international law and political issues discussed in the other answers; political discretion in a s 115.1 prosecution is maintained by the requirement for that the Attorney-General's consent is required for such a prosecution: s 115.6.
France's penal code applies worldwide to any offence where a French national is a victim: Penal Code, art 113-7. The French Code has a general defence of lawful authority: art 122-4, but I don't know French (or French law) well enough to say how a French court could would look at a US law permitting capital punishment.
Cavelese cable incident in Italy in 1998 can be a good example, American Marines were having fun while flying far below the prescribed height and it turned into an ugly accident. Italy didn't received the jurisdiction to try those marines despite of the fact that the incident took place in Italy. Getting hold of something in France which happened in America and considered legal by America is really far fetched.
