Did you specifically ask for tap water or did you just say "water"?
Because in France, technically there's no legal obligation to offer free water. Unlike Belgium or other countries, it's not written into the law. So restaurants can totally refuse to serve tap water for free, and lots of them take advantage of it since it's an easy source of income. It's completely legal, just a different cultural/commercial thing.
That said, in restaurants that are a bit more laid-back or less uptight, if you explicitly ask for "tap water please" (or "carafe of water" in some places), they'll serve it to you without fussing. But yeah, the waiter who directly offers you Evian is doing it because it's in their commercial interest. It's not specific to that restaurant in Lyon, it's pretty widespread in France unfortunately.