Validity of French rail tickets after stamping

It depends.

The short answer is "24 hrs of validity from compostage, if you are lucky"

If your ticket includes a reservation for a mandatory reservation train (i.e., TGV, Corail Lunéa, Corail Téoz, international services...), then you must use it only on the train specified on the reservation -- it is not valid on any other train on the route, regardless of whether the other train has mandatory reservations.
Obviously, you cannot use a mandatory reservation train without reservation, however many ticket types allow you to exchange up to the time of departure, and there are indeed machines on many station concourses that can issue exchanges, if you don't fancy queuing for the guichet.
If you are on non-reservation mandatory services, with an unreserved ticket, then the ticket is valid from:
- 24 hrs from the time of Compostage (stamping), or
- 24 hrs from the time of your first train, in the case of an e-ticket or print-at-home ticket.
If your break of journey pushes you from one fare calendar colour into another (i.e., pushes you from off-peak to peak), you'll need to have a peak (white) fare ticket, as the only occasion that this is not required is when you change onto the next available train (i.e., don't break your journey)
And I should mention that aller-retour (return tickets) explicity state that you must use the same route on your return portion. It is possible to tell, because you pay per km, so the price will differ. Circular tickets exist for some flows, but you have to nominate a start / end station when you buy them.

I believe tickets in Île-de-France (Greater Paris) have separate conditions, as ticket prices, validities, etc. are determined by STIF rather than SNCF. You may also find that some other cities have separate arrangements for local trains, particularly if the city in question is running a tram-train service in place of traditional services.

Finally, I should note that this is based on my own personal translation of French legalese. You should check with a guichet.

 

I disagree, the language in the "General Conditions of Sale for Travel Tarifs of SNCF" (accessible here http://www.voyages-sncf.com/services-train/guide-voyageur ) or by direct link at http://a1848.g.akamai.net/f/1848/75.../design/guide/dispositions_Generales_SNCF.pdf
says

Which I translate as
3.3 Delay in using transport tickets
The journey must be terminated within the 24 hrs which follow the stamping or, in the case of an e-ticket or a print-at-home ticket, in the 24 hours following the date and time of departure of the train.
In the case of a stop in the course of the journey in excess of 24 hours, or if the multiple stops cause you to pass the hour limit of the ticket, the journey is split into as many journeys which necessitate the production of distinct tickets and are susceptible to give rise to an excess charge.

My french is a little rusty, but I see no mention of midnight next day.

Old (orange) composteurs used to only print the date and the station, so in effect you had until midnight next day (as nobody could tell). The new yellow ones print the time as well, so perhaps that is where this idea came from.

 

If your ticket is printed in several portions for your journey, make sure you validate (composte) all portions. I got "British staff? you should know better!" from one Corail guard, who luckily saw the funny side of it.

Zut Alors!