The best source for mathematics research is MathSciNet, the online version of Mathematical Reviews, which indexes and reviews the mathematical literature since 1940. Over 80,000 new items are added each year, most of them classified according to the Mathematics Subject Classification.
There are two places to search MathSciNet. The content is the same but the interfaces are different.
Use these indexes and databases to find journal articles in French. Both scholarly and popular articles may be included.