They are both at 7-under-par 135 after two rounds.
Lynn, who began the day in a tie for 28th place, shot up the leader-board Friday with a 6-under 65 while Larrazabal, the first-round leader by one stroke, managed 1-under 70.
Lynn sank a shot from the bunker for birdie at No. 18 to grab a piece of the 36-hole lead.
"When I made a double bogey seven on the ninth I wasn't happy at all, but I knew that I was playing well," Lynn said.
"I started off a little tired because I was watching the match and I was a little nervous so made a bogey on the first," Larrazabal said after a windy day at Le Golf National golf course.
Colin Montgomerie (68) and Lee Westwood (68) joined a group of five players tied for third place at 5-under 137.
Toddler uninjured after being knocked over by Obama family dog
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'