As alternative, you can use blablacar.fr.
This is a system where people who have empty seats in their car put them on a web site named blablacar.fr
It is pretty usefull when the train are on strike. On the top of that it is quite cheap.
The other alternative are the buses (
www.flixbus.fr or
www.ouibus.com) as Le Mans is not far away from Paris it will not take much time.
Regards,
Tique