For a more recent case than Joan of Arc (which was hardly a trial by nowadays' standards), have a look at the infamous "Affaire d'Outreau" which was really a huge scandal at the time.

I personally think we just talk more about the USA because: - everything the USA does or says is heavily scrutinized anyway, - many more people can read English than French or Russian so news about cases like this one are more shared on social networks, including among foreign people.