If your train is canceled, you will be offered a means of substitution, generally the next train on that line that has enough room. Talk to the conductor if you need to meet a connection. There is generally no problem with boarding a later train if yours was canceled, except that if the next train is over capacity as a result, you may be asked to wait longer.
The same applies for major delays. Ask conductors if you need to make a connection. It's even possible to get reimbursed for a taxi if you miss your last bus home; nonrefundable plane tickets might be another matter.
There is a compensation program. You need to contact the appropriate service. There are several conditions to get a compensation.
- You get 25% back if the delay is more than 30 minutes, 50% for more than 2 hours, 75% for more than 3 hours' delay.
- The program only applies to long-distance trains (Intercités and TGV, and some international trains), not to TER (regional trains) or suburban trains.
- I thought there was a requirement that the trip is more than 100km, but I see no such requirement on the SNCF website now, the rules may have changed recently.
- This only applies if the delay is due to SNCF. Notable exclusions include vandalism, extreme weather and strikes.
- The rules for international trains are different.
Often, when SNCF assumes responsibility for the delay, there will be people handing out envelopes at the arrival station. If there aren't, ask at the station office. Fill in the form, put the ticket in the envelope (plus the note that says you were in a delayed train, which is mandatory if your ticket doesn't include a reservation) and send the envelope by mail. I don't know how that works if you don't have a bank account in France, there might not be a reasonable option to get the money.