I already had @graham's setting made but still found issues using certain web apps like forums.
For example, the Sublime Text forum does not give you the right character for a cedille when you type a 9 on a French keyboard.
A similar miscoding occurs on a financial matters forum.
When some member of these forums has a user name which contains an accented character, I see a Cyrillic character instead when viewing the site on my PC - but I observe the correct character when viewing it on my Android phone !
Others report the same thing.
Some people suggest a browser fix, i.e. not allowing the browser to use the fonts assigned by the website designer. This is not the solution at all: it limits the user experience of the site, where font choice is a deliberate aesthetic choice, and ignores the real cause of the problem. The real cause of the problem in my experience has been the use of Helvetica as the main font or as a fallback font if users haven't the main one installed.
So this leaves us the option of removing Helvetica and letting the browser fallback to the next available font in one's system. Font Manager seems to have a problem removing Helvetica so you need to remove all files associated with this font's installation.
UPDATE
Reinstalled Helvetica and Helvetica Neue fonts. No Cyrillics now.