The trains exist, but they are not as useful as in country trains. Just getting a ticket can be tricky as not everyone will sell them. Most train systems assume you are going to the major city in their country, (Paris) and so the routes do not always make sense for other trips. One train per day (or less) is not good service. Cross border makes it much more likely you have to transfer to a different train and the poor on-time performance of some nations becomes a problem.

There are not border controls which is nice. However there are a lot of other things that can go wrong. Some routes work much better than others. Europe is a big place with lots of different trains systems if you only went on the good routes you won't have a problem, but there are a lot of routes that are not as good - and many more routes that should exist but do not at all.