I think, most of songs that young Russians listen to is in English or Russian. Sadly, because diversity is good.
Clearly some Russians know modern French and Italian rock/pop/rap/anything, but.... first I don't really know what is popular in Russia today, second, I hardly can remember a situation when young people discussed anything French or Italian in my presence:( Well, if it was "German" I would guess Rammstein is still the most popular:)
So I think, the "most popular" stuff is still things from 40s - 70s:
for Italy it is clearly Celentano - and various opera singers (shoudl I name them?:)), for France Piaf, Dassin, Aznavour and so on. Mathieu. Yves Montand.
French and Italian learners in Moscow know Georges Brassens (French) and Fabrizio de André (Italian), both are singers-songwriters. As I said, I personally love Brassens: clear pronunciation and interesting enough lyrics so that you want to understand what he sings about. But again he is classics.
French= Claudio Capeo, Chilla, Stromae, Indila, Nekfeu...