Montpellier lost 2-1 at home against Arsenal on Tuesday and have only picked up four points from five league games, but they were upbeat after pushing their illustrious opponents close.
"You can't be happy when you lose but we shook one of the best teams in Europe. Physically and mentally, we are there," said Girard, whose side host St Etienne on Friday.
"In terms of intensity and aggression, we played the best half of our season," he added of the second period against Arsenal where they hit the post as they strived for an equaliser.
Goalkeeper Geoffrey Jourdren said the club's first Champions League encounter was a positive experience despite the result.
"We were in the right state of mind. This defeat will help us," he told reporters.
Paris St Germain, who have spent more than £120 million transfers since they were taken over by Qatari investors in April 2011, are expected to snatch their third league win in a row at promoted Bastia on Saturday.
PSG, who trail leaders Marseille by six points, demolished Dynamo Kiev 4-1 in their Champions League opener on Tuesday.
Coach Carlo Ancelotti could make a few changes to his team including resting Zlatan Ibrahimovic, who said he was still suffering from an ankle sprain he picked up last month.
"I still suffer from the injury I have since the start of the season," the Sweden striker said on Tuesday after scoring the opener against Kiev.
Centre back Mamadou Sakho could play having overcome a minor injury as Ancelotti said he was tempted to start rotating the central defenders after Brazilian pair Thiago Silva and Alex played in the Champions League.
Marseille and Lyon will continue their battle for top spot on Sunday when they play against Evian at home and at 2011 Ligue 1 champions Lille respectively.
Both clubs are involved in Europa League action later on Thursday, the French champions away to Fenerbahce while Lyon welcome Sparta Prague.
Marseille have made a perfect start to their league campaign with a maximum 15 points from five games and lead second-placed Lyon by two points.
Lille, who slumped to a surprise 3-1 home defeat against BATE Borisov in the Champions League on Wednesday, have only won one league game this season and are nine points off the pace.