I love trains (not in a weird way
), as they can be really relaxing and if you don't mind taking longer to get someplace, they are a great means of having a nice trip, with the added bonus of having some scenery, but as much as I wish undersea train networks existed, while possible, it's not worth making them due to the insanely high upkeep costs that come with it. However, for relatively small distances, they could be a thing, but nothing even remotely close to international (assuming you mean overseas travel between continents. The most that could be effective would be something like Denmark with Sweden at the part where it's close enough to ferry across, beating the purpose of even making the whole project honestly... For actual overseas travel, plane is the best option. For continental travel, trains are fine and there is even the intercontinental express that runs all throughout Russia and some neighboring countries connecting Europe with Asia.
Well, technically the Eurotunnel is already there, proven, international, and a train
While the Eurotunnel exists, it was a special case and that's the only reason it was actually attempted as a project. There were already cave paths running underground, which minimized the work needed for it and with the natural cave system supporting the railway the upkeep costs are minimal.