I can read French, et je peut l'ecrire aussi mais c'est pas facile sans faire des faute. Donc je vais répliquer an anglais.
I've traveled with rep 126610ln submariner outside of EU. It has not been an issue, you just put it in the box that goes through the scanner.
Although, where an issue may arise, is when walking to the "nothing to declare" or "declare" path.
Legally, depending on which country, you're not allowed to travel with more than X in cash and other valuables. Unless you declare (and pay taxes) even though it is your watch, which you've bought and already paid taxes on.
It depends too much from country to country, but it could be an issue.
This case is the first that comes to mind:
Arnold Schwarzenegger detained over EU tax for luxury watchBBChttps://www.bbc.com › news › world-europe-68015612
BUT, I also know a case where a Belgian business man traveled to Switzerland, after a successful deal he bought three rolexes. One for him, one for his wife and one for his daughter.
There is no VAT on luxury watches in Switzerland when they're for export. (OR you can choose to pay the WOEST fee, but you don't have to).
The man arrived at Belgian airport, walked the "nothing to declare" path, and was pulled aside, inspected, they found three rolexes in his luggage -> had to pay 21% VAT + fine.
He could have prevented this by simply paying the (I think 8%) WOEST in Switzerland.
So yes it's possible, doesn't happen frequently.