Hah! We had the same situation taking a train from Marseille to Paris. Looked at the seats, entered the proper carriage, sit down, and at the next stop someone came and told us we took their seats. I was like 'this is 74B' (or whatever), 'the ticket is for that seat', until someone managed to tell us that we got in the wrong part of the train, and we need to move forward.

Now, the train itself was two trains connected together, and at the next stop we literally had to run like 100 meters or so to make it on time to enter the front part, because there was engine near the end/stop.

Not sure would the 2nd half of the train depart, but it was super stressful experience.