The Welsh region looked set to leave Stade Marcel-Michelin empty handed after a two tries from wing David Strettle and further scores from Aurelien Rougerie and Wesley Fofana gave the hosts a full five-point haul.
But, with time running out, the Welsh region created a try for replacement hooker Sam Parry and immediately attacked from the restart where Biggar sent Tom Habberfield racing over.
With Justin Tipuric and Eli Walker having already scored, it meant the Ospreys picked up a point for a four-try haul and another for losing by less than seven.
The result keeps them at the top of Pool 2 ahead of the December double-headers, in which they will face Bordeaux-Begles home and away. Next up though is a regional derby with the Cardiff Blues.
“To come away from one of the most difficult place to play in Europe with two points is like a win for us, really,” he said. “I thought we showed a tremendous amount of bravery out there. We knew coming here that it would not be enough to just play for penalties and drop goals.
“We had to be positive, we had to be confident enough to play and try and put them under pressure. We did that but they stood tall towards the end of that first half and we could easily have let things slide away there.
“But we knew we had to keep playing our game and chance our arm. It if had ended with us losing by 40 points then at least we would know we had given it a go.
“We managed to get the balance right and took our chances well. We could have dropped our heads and it is a huge testament to our spirit that we finished those chances at the end.”
