Gasquet was one of two French winners as qualifier Kenny De Schepper put out Portugal's Gastao Elias 6-2, 2-6, 6-3 to move into a second-round meeting with Gasquet.
Spain's Pablo Carreno Busta advanced over Constant Lestienne of France 6-3, 6-1.
Gasquet has played a pair of finals in Portugal, losing to Novak Djokovic in 2007 and Juan Martin del Potro in 2012.
Gasquet last took to a court on cement in Indian Wells on March 15, retiring with a herniated disc in his back against German Michael Berrer in the second round.
The 28-year-old improved to 11-4 on the season after his winning debut on clay. "I'm feeling better, it's as important for me to finish the match as win," said Gasquet.