This is a list of carriers that support the Apple Watch and the models the carrier supports.
https://www.apple.com/watch/cellular
It is possible that the Series 9 and the Ultra 2 "MAY" (or may NOT) work across the Atlantic. As fellow users we do not have sufficient experience to say for sure that it will work. If you decide to try this, then please let us know. If you are coming back to the U.S. within the 2 week return period, you could try it and return it if it does not work. If you will not be back for months, then do not experiment with your money that way.
The Series 8 and older WILL NOT work across the Atlantic.
NOTE: warranty is country specific because of different warranty laws in every country. So unless you travel to the U.S. frequently, if it breaks, you get to pay for the repair, even if it warranty would normally cover the repair.
Some countries restrict the feature(s) allowed on the Apple Watch (should not be an issue for U.S. model), but you should check to make sure the feature(s) you desire will work on the model you buy
https://www.apple.com/watchos/feature-availability