Sad to say, but very few people record the serial number of their bike. Thus, when it gets stolen, it's next to impossible to identify it.
That's why we do a registration program here when we rent the kids a lock; we also put numbered stickers on the bike indicating that it will be in the database if stolen.
If you are serious about checking, you could have the local gendarmes run the serial number through NCIC, but that won't prove anything conclusively.
A few other dodges; put your name, adress, etc on a piece of paper and put it inside the handlebar.
Use an engraving tool and put your SSN or other identifier in a hard-to-notice spot like the seat tube inside the frame, the inner side of a crank arm, or somesuch. Makes it easier to identify if stolen. Hard to believe, but many victims can't even tell us what brand or model their bike was. "Uh, it was red..."