The Gunners found themselves behind at half time courtesy of a Mathias Autret strike, and it took until the 82nd minute for them to reply as Alex Oxlade-Chamberlain stylishly rescued a point for the visitors.
Arsene Wenger named a smattering of youngsters in his side for the game, and two of them combined midway through the opening period when Alex Iwobi found Jeff Reine-Adelaide, who could only curl his effort wide of the target.
The hosts took a surprise lead with seven minutes remaining of the first half, though, as Zoubir raced onto a loose ball and squared it for Autret, who applied the finishing touch from close range.
That was how it stayed until half time and, despite making six changes at the interval and enjoying the lion's share of possession, the Gunners struggled to find a way through after the break too.
Arsenal soon began to apply the pressure, though, and Douchez was called into action with 15 minutes remaining when he tipped Theo Walcott's shot around the post after good work from Oxlade-Chamberlain.
It was Oxlade-Chamberlain himself who got the equalising goal, though, and it came in some style as he was played through before producing an audacious chip over the keeper to level things up with eight minutes remaining.
The hosts pushed on in the closing stages looking for a winner, but in the end both sides were forced to settle for a share of the spoils as Arsenal got their pre-season off to a low-key start.