Alessia Russo put Arsenal ahead shortly before half-time before Georgia Stanway doubled the visitors' advantage five minutes after the restart.
Paris FC responded through Clara Mateo in the 72nd minute, setting up a tense finish before a bizarre late incident handed the French side a penalty.
Leah Williamson picked up the ball inside the penalty area during what Arsenal believed was a goal-kick situation, but referee Iuliana Demetrescu awarded a handball penalty after determining that goalkeeper Misa Rodríguez had already taken the kick.
Maeline Mendy converted from the spot in the 87th minute to complete Paris FC's comeback and deny Arsenal victory.
Russo opened the scoring in the 41st minute after combining with Stanway before firing into the bottom corner. The goal ended her wait for a first strike of the season.
Stanway then made it 2-0 in the 50th minute, controlling Emily Fox's cross before finishing emphatically from close range. It was her first goal for Arsenal since joining from Bayern Munich in July.
Paris FC continued to threaten despite Arsenal's advantage, and Mateo eventually reduced the deficit after breaking forward and rounding Rodríguez before finishing into an empty net.
The late penalty then allowed Mendy to level the contest, leaving Arsenal with a point after they had appeared to be heading towards their second Champions League victory of the campaign.
• Paris FC: Clara Mateo 72', Maeline Mendy 87' (pen)
• Arsenal: Alessia Russo 41', Georgia Stanway 50'
The draw leaves Arsenal with work to do in the league phase, with matches against defending champions Barcelona and eight-time European champions Lyon still to come. UEFA had recorded Arsenal's opening-round victory over HB Køge as a 1-0 win after a 93rd-minute Mariona Caldentey penalty.