Both players eclipsed the course record at the Oitavos Dunes Golf Course with matching scores of 8-under-par 63.
Martin's eighth birdie of the day at the par-4 18th hole lifted him into the overnight lead with Bourdy.
Early front-runner Gonzalo Fernandez-Castano of Spain, one of five players to shoot 7-under 64, was in the clubhouse when he was joined by Sweden's Michael Jonson and fellow Spaniard Jose Manuel Lara at 7-under 63.
"I had a 62 in the Pro-Am, but I never expected 64 today," Fernandez-Castano said while watching the round's ending. "To do it you have to hit all the shots well and that's what happened."
A total of five golfers bettered the tournament's previous best score with 79 players within earshot of the lead at par 71.