I’m French and I’ve had tons of dental work done. Tooth removal, a large number of root canals, capping, crowns, etc…
French dentists use novocain all the time (what they never use, though, is nitrous oxide), that is, when you might actually feel pain. You probably already have had a root canal done on this tooth, and without a nerve, the dentist can do pretty much anything to your tooth, and you won’t feel a thing.
It’s probably by random chance that when you had dental work done in France, it turned out that both time, the dentist was working on a desensitived (it that a word?) tooth. Believe me, because it happened to me once, if a dentist is trying to drill into a tooth that still has a nerve, you’re going to scream. Regardless of whether the dentist is French or North-American, regardless how skilled he is.
Similarly, I doubt that American dentists actually use novocaine when your tooth isn’t sensitive.
And regarding the OP : no, having a tooth capped doesn’t hurt. In fact, with anesthesics, pretty much nothing done by dentists hurt. Except for removing a tooth, and even that doesn’t always hurt.