Lajciak: Thanks for the advice. I would like to learn French. A fair number of games seems to be translated to French, but it might be somewhat difficult to pick a game originally designed in French, as it seems that French-owned publishers/game studios (if I remember correctly Ubisoft, for example, is French-owned) tend to produce games originally in English. Plus of course, it has to be a game I enjoy, lest it kill the motivation, which limits the pool of games further.
You make a good point about the comparison with movies. I certainly cannot at this stage watch a movie in French with a sufficient degree of understanding to make it comfortable. It might mean that I am not ready to take the plunge into French-language gaming, though many games have the option to turn on subtitles, which could lower the barrier substantially, as reading is easier than listening. Hmm, an alternative could be to have say French voiceover and English subtitles or vice versa, but that might defeat the purpose, as the temptation to rely on the English mode would simply be too great.
Try to find something where you can replay the same audio several times, in case you miss it and want to hear it again. Maybe a classic point & click adventure? Or games where conversation advances slowly and you can have time to mull over the previous sentence before moving to the next.
I'm lucky, I guess, that I tried this with Japanese: plenty of native titles to choose from, and their native visual novel style allows to listen on sentence at a time and repeat it as many times as I need to understand it. I was never able to use games to learn Dutch, though. I guess the game approach will work better on some languages than in others.
This doesn't mean you can't use it all though. Even if there's no perfect game, you can still give it a try, maybe it works for you. I'm just giving a few tips that hopefully allow you to make the most of your try.