PSG host relegation battling Le Havre on Saturday
The Gunners dominated the opening 20 minutes but Boro should have led by halftime. Adama Traore broke clear but Petr Cech saved his shot with legs and Alvaro Negredo wasted a great chance from the rebound.
The hosts had another let-off when Gaston Ramirez's curling free kick thumped against the post and Ramirez headed a great chance straight at Cech.
Arsenal were better after the break and Boro keeper Victor Valdes made a superb save to keep out former Barcelona team mate Alexis Sanchez's dipping effort before Mesut Ozil had a late goal disallowed for offside.