Most train tickets in Europe are subject to the
GCC-CIV/PRR terms of use.
Originally Posted by GCC-CIV/PRR
5.2.6 [...] Reserved accomodation must be claimed within fifteen minutes of departure of the train from the station from which the reservation was made or the passenger may lose his claim to the accommodation.
In other words, if you don't claim your seat within 15 minutes from departure from Paris, your reserved seat may be sold to someone else. I think that you are still allowed to travel, just without the right to sit down during the journey.
Unless the train company's own terms of use states otherwise, assume that the GCC-CIV/PRR terms apply.