The 34-year-old bagged his 43rd and 44th goals for his country, taking him to within seven of Les Bleus’ all-time record scorer, Thierry Henry, on 51.
Giroud rifled a powerful finish into the near post in to draw his side level after going a goal behind in the first half, and powered in a diving header from Kylian Mbappe’s cross just before the hour mark.
The striker’s double comes as speculation over his exit from Stamford Bridge gathers pace.
French outlet Telefoot Chaine report that Giroud has decided to leave Chelsea in January.
The experienced forward has played just 33 minutes in the Premier League this season as he is unable to get in ahead of Timo Werner and Tammy Abraham.
The World Cup winner will have playing time at the forefront of his mind with the rescheduled Euros coming up in 2021.
Speaking earlier this week, France boss Deschamps urged him to change his situation before the next international break in March.
‘Olivier Giroud knows it – the situation he’s in today cannot drag on forever. Before March he will have to find another situation than this one,’ Deschamps told French radio station RTL.
‘Today, it is not good for him. Will it stay the same or will it improve? It’s up to him. He knows what I think, even if I don’t forget everything he has done and everything he would still be able to do.’