Evans, seeded fifth, needed only 75 minutes to dispatch the Frenchman 6-2 6-1 as he chases his first tour-level title of the season.
The 32-year-old won 82 per cent of his first-serve points and broke five times to take the win.
Jack Draper put up a brave fight against top seed Hubert Hurkacz of Poland but fell 7-6 (5) 6-7 (5) 6-1 to the world number 11.
Second seed Felix Auger Aliassime will be in action on Thursday, taking on Manuel Guinard for a place in the quarter-finals.
At the Stockholm Open, it was a gruelling afternoon for second seed Cameron Norrie but it ended in a 150th tour-level win for the 27-year-old.
He eventually overcame Aslan Karatsev 6-7 (8) 6-3 6-4 in a match which took more than three hours.
"It was a tough match," said Norrie. "Every time Aslan was down he raised his level and he really stole that first set from me.
"I had a couple of set points and I didn't execute as well as I could have done in the tie-break.
"I stayed solid and I was a bit frustrated in the third set but I managed to claw it back. I feel good and fresh."
Top seed Stefanos Tsitsipas also had to battle hard against American Maxime Cressy in his second round match, coming through two tight tie-breaks before sealing a 7-6 (7-5), 7-6 (14-12) victory.
Also still alive in the tournament is third seed Frances Tiafoe, who faces Sweden's Elias Ymer on Thursday.