Here in Paris I've seen that happen quite often. The seniors have a card identifying them as such, which they sometimes show when they ask for your seat. Sometimes they'll even ask people for seats that are not designated (I always offer mine anyway, but many people don't).

Last week on a crowded bus I watched an elderly woman ask a 50-ish man for the senior seat he was sitting in and he actually refused even after she showed him her ID card; he just grumbled something about being a war veteran and went back to reading his paper. Another man sitting nearby offered her his seat instead. This is the only time I've ever seen someone not move; usually people are more considerate or at least cooperative.

Anyway, if you come to Paris and use the buses or metro, don't hesitate to ask for a seat if you need one. The designated seats are indicated by orange stickers on the wall.