I'll be training it in and out of Le Mans Station as well and haven't used the trams before either.
I asked a similar question over at
www.beermountain.com and got quite a few helpful answers there. I'd expect the trams to be pretty rammed after the race as they're popular with locals as well as foreign racegoers, so I'm planning to buy a weekend pass at the railway station when I arrive which means I won't need to be waiting in line for a ticket and can just get on the first available tram when it's time to go.
I've also booked myself on a train leaving Le Mans for Morlaix at 7pm on the Sunday (my ferry sailing is from Roscoff at 0830 on the Monday), so I'd recommend booking your train out (if you haven't already) maybe for a couple of hours after the race ends so that you'll have plenty of time to make the trip (which is about 20 minutes by tram) from the circuit to the main railway station.