Train connection times

The online schedules usually only provide feasible connection options, but you should also be waiting by the door of the train with your luggage before it comes to a final stop. I assume that this question is a follow on for your route Paris to Chamonix and Chamonix to CDG Paris airport. Looking at the DB schedule link, the only 3-minute connection I see is at Martigny (Switzerland) on the way to Chamonix; the next departure that you can catch if you miss it is probably one hour later (last one at 18:45). That route around the lake is scenic, although some routes via Lyon or Chambery can be done with only one connection.

It depends where, and how big the station is. As Laura says, the website wouldn't have suggested the connection if it wasn't possible (at least if you don't dawdle). In many cases it is a timetabled connection, and the second train will wait, as long as the first is not unreasonably late, and in that case you just catch the next train one hour later.
In many cases for small stations, and I suspect that may be your case, most of the passengers will be changing from one train to another, and the second train is sitting in the station waiting for the first train. It says 3 minutes, but what it means in practice is that the two trains stop side by side, and the second train is sitting waiting for the passengers from the first. Once they are all aboard, it starts off.

The unequalled "Man in seat 61" site has a detailed explanation: http://www.seat61.com/Europe-train-travel.htm#How_long_to_allow_for_connections_between_trains

Wow - that Seat 61 explanation is superb. I'll just emphasize that there is no set time in France or any other country - it depends exactly which station and which trains are involved, just as he explains.

For me, a great deal depends on whether I'm encumbered by a suitcase. There are a lot of stations still without elevators (don't know about France specifically). Finding and using an elevator would probably be even slower. I think there are some Swiss connections I would not book on days I was carrying a suitcase.

That said, I've never missed a train connection in Europe, though I've had to move quickly in Switzerland. I have, however, come close to doing so when I didn't pay enough attention to the platform/quai/gleis/binario displayed on the departure board. If the platform is listed as a number followed by a letter, seek help. Platform 1n (1e, 1s, 1w) is not the same as Platform 1. It may be quite a long walk away!

Switzerland is no way compares with any other train systems that I've ever been on in Europe. The Swiss System is by FAR the most superb in all of their workings. The French on the other hand...definitely not near the top! I keep my expectations low when it comes to French trains. If they're actually running and not on strike or protest I consider it successful day!