Ricardo Faty had two early opportunities for the hosts as he blasted his free kick over the crossbar before missing the target with a header from a corner.
PSG created few chances in the opening 45 minutes as Nene's speculative free kick flew narrowly over.
Ajaccio came closest to breaking the deadlock eight minutes into the second half when Eduardo's shot hit the post.
In what was a heated second half, PSG manager Carlo Ancelotti was then sent to the stands by the referee for kicking a bottle in anger following a decision.
The game then took a bizarre turn as play was interrupted during the second minute of added time when the floodlights went out.
Light was then restored before the match was finished without a goal.