The hosts' attempts to hold off PSG were undone by a defensive mistake in the 25th minute when Alexandre Lauray's pass was blocked by Goncalo Ramos on the edge of the box. The ball reached Doue, who buried it into the bottom left corner.
Substitute Barcola doubled the lead in the 71st minute as he got hold of a lofted ball from Nuno Mendes, sprinted into the Le Mans box and finished at the near post.
Leaders PSG host third-placed Monaco in a Ligue 1 clash on Friday.