I just ordered some Vittoria Voyager Hyper 700c x 35 (measures 37 on the rim & inflated) for my '85 Nishiki Riviera Mixte. Right now it's got 32 Panaracer Paselas which are fine, but I wanted solid black and a cushier ride. Ordered the tires & still waiting.
As others have said the word "Mixte" implies "unisex" or "mixed" and was meant for riding by anyone. When the design became more popular in the US, marketers aimed these bikes at women. A bike is transportation & fun. Just go for it.