England duo Alessia Russo and Georgia Stanway scored either side of halftime in Paris on Wednesday (Thursday AEST), which looked like it would hand Arsenal a second straight win in the competition.
However, Clara Mateo reduced the deficit with 18 minutes left, before Williamson was penalised for handball inside the area when she thought the game had not yet restarted. It resulted in a spot-kick for Paris, which Maeline Mendy converted to ensure a share of the spoils.
Australia's Kyra Cooney-Cross played the whole match for Arsenal, and despite having a solid game was unable to help her side to victory.
Chelsea and Lyon missed chances at either end as they drew 0-0 at the OL Stadium in France.
The Blues were denied two penalties after Sjoeke Nusken and Lauren James were seemingly felled inside the area, but referee Marta Huerta De Aza ruled both out after being sent to the VAR screen.
Salma Paralluelo saw an effort ruled out for offside, and James and Ada Hegerberg both spurned late chances, which meant the sides continued their respective unbeaten starts to the competition.
Matildas star Ellie Carpenter took the field for Chelsea, her passing a highlight throughout the game.
Barcelona made it two wins from two after they thrashed Roma 6-0 courtesy of braces from Caroline Graham Hansen and Claudia Pina, alongside an own goal from Shukurat Oladipo and Ewa Pajor's late strike.
Bayern Munich left it late to pick up their first win in the competition with a 3-0 win over Benfica.
Klara Buhl's 74th-minute effort broke the deadlock to give Munich the lead, which finally blew the doors open, and further goals from Pernille Harder and Franziska Kett ensured a comfortable win.
Second-half goals from Tatiana Pinto, Emma Stolen Godo and Alba Redondo gave Juventus a 3-0 victory over Hacken, the first win of their Champions League campaign following defeat last week.
