SEAT RESERVATIONS UNAVAILABLE from lourdes to Parts Montpranase

I think it's the end of school holidays an Paris, and most TGVs are already fully booked. On 7 May, for 4 persons, there's only the 7:04 TGV left in first class (price for 4 persons with a 2nd class pass):

The above screenshot only shows connections with available seats.

An alternative could be something like this:

The train from Toulouse 10:31 to Paris 17:19 still has seats left; you can book them via Belgian railways, price is 20€ per person.