Yep, I'm french and I still call them baskets. And it's true we sometimes say "shoes", it was kinda in a tongue in cheek way at first but it became more natural for some.As a British guy, they've always been trainers to me. That feels right. They're shoes you do some kind of training in.
I spent a lot of time in France growing up, though, and I went to a French-speaking school. Over there they're called tennis shoes or, at least when I was a teenager, "baskets" - as in basketball shoes. Sometimes French kids also just call them "shoes," as in the English word, not "chaussures".
The only one I know who calls them "tennis" is my grandmother who is almost 100 years old.