Illegal as a standard practice
Driving cycles in a fairly dense pack falls afoul of article R431-7 of the code de la route:
Les conducteurs de cycles à deux roues sans remorque ni side-car ne doivent jamais rouler à plus de deux de front sur la chaussée.
Ils doivent se mettre en file simple dès la chute du jour et dans tous les cas où les conditions de la circulation l'exigent, notamment lorsqu'un véhicule voulant les dépasser annonce son approche.
Cycle riders must never ride more than two abreast on the road.
They must move to single file once night falls and in any case where road conditions require it, in particular when another vehicle signals its intention to overtake.
But this is a "protest" or a "sports event"
Protests and sports event routinely obstruct traffic more than usual, and that’s ok, but it comes with other rules.
Assuming there are more than one hundred riders, this falls under article R331-6 of the sports code ("sports event taking place on a public road"). Even if there are fewer than a hundred riders (or if one wants to dispute the meaning of "sports event"), this probably falls under the general definition of "protest" as per article L211-1 of the internal security code.
The consequences are basically the same: the event must be declared in advance to the local authorities by a certain date, with details (who are the organizers, the expected number of people, the date and place, etc.). The authorities may forbid the event if "the planned event is of a nature to trouble public order" - what this means in practice is left as an exercise to the courts, and more than one national or local government have been suspected of forbidding events for political reasons. Oftentimes there is a negotiation between the local authorities and the organizers (what about going through road X rather than road Y, do you have first-aid staff on site, etc.). My two cents: the system basically works, because the government used sparingly its power to forbid protests and hence that power is seen as legitimate, but it would not take much for it to collapse (see for instance the New Caledonia protests where Paris is definitely not seen as a neutral arbiter; or see the Orange marches in Northern Ireland, where the British state tries very hard to delegate any tough choices to local actors for obvious historical reasons).
The important concept here is organizer. Article 431-9 of the penal code means that whoever organizes an event without declaring it, or with a fraudulent declaration, or in spite in an interdiction, is criminally liable. Deciding who is an organizer, in the cases where the event was not declared (or was declared by Mr. X, but then Mr. X said it was cancelled, and a bunch of people still turned up) can be a tough exercise left to the courts. Let us suppose there are no organizers.
Attendance is generally not criminalized (he only specific infractions are participating with one’s face covered, 431-9-1, or wearing a weapon, 431-10.) Beyond the possibility to prosecute for road code violations (see above), the police may also disperse the crowd; that is, they give warnings to attendants to go their separate ways obeying certain forms. Staying after two warnings to disperse is an infraction (see articles 431-3 and following of the penal code). I am not exactly sure how that would apply to cycling events (dispersion orders are mostly tailored for static events, where a rowdy crowd is occupying a given plaza or street) but there is nothing in the statute that says it could not apply to a moving group of cyclists.
