The England center-back volleyed home from close range after he latched on to a well- timed cross from the other side.
They did not give many more clear-cut chances, but they defended well.
A strong defensive performance allowed them to beat last year's semi-finalists.
The head coach of the Blues is currently recovering from an emergency hysterectomy as she battles with endometriosis.
Fran Kirby was missing for the trip to Paris.
Despite the hostile atmosphere created by the ultras, they rose to the challenge and produced a positive result.
The noise of the crowd was so loud that it was impossible to hear anything else.
For the first time in 16 games, the hosts failed to score.
They didn't have last season's French league top scorer, Marie-Antoinette Katoto, who tore her anterior cruciate ligament at the Euros.
Bright rifled a cross into the roof of the net after peeling off her marker.
As the European campaign got off to a winning start, the engine was Scotland'sErin Cuthbert.
She was involved in the middle of the park throughout the game, playing a key role in keeping Paris Saint-Germain at bay.
The threats they would have posed on the counter were nullified by her efforts.
She helped to steady the play and allow the Blues to move forward with her help.
She has been used in both attack and defence before.
In her previous work as a winger, she was able to find Bright at the back post by deftly following up a failed corner.
Her work in front of the defence aided Bright and Kadeisha Buchanan behind her to produce a steely performance and limitGermain to only one shot on target.
It was a stark contrast to their last appearance in the competition, when they were thrashed by Wolfsburg in the group stage.
Paul Green spoke before the game of getting back to basics and they did it.
It was their defensive efforts which enabled them to edge one of Europe's strongest teams and bode well for the chances of progressing.
Last year's quarter-finalists Real Madrid are likely to make it a three-way battle to qualify for the knockout stages. Next up for the Blues is a match against Vllaznia.