Well, it looks like the direct Strasbourg - Le Mans service is fully booked. A lot of the trains are.
There's a Stuttgart-Paris service at 08h55 tomorrow, going for €116 on bahn.de, arriving at 12:35. Allowing an hour to transfer from Paris-Est to Paris-Montparnasse (straight run on metro line 4), there is then a 14h25 train for €40 on voyages-sncf.com, arriving in Le Mans at 15h18.
Both are TGV services, so need a reservation.