The 31-year-old had been with Rovers for over four years and follows former fan favourite Morten Gamst Pedersen, now playing in Turkey, in departing Ewood Park after he left 24 hours earlier.
Givet made 133 appearances for Blackburn but found himself surplus to requirements with boss Gary Bowyer keen to change the direction in which his squad is heading.
Speaking to Rovers' official website, Givet said: "Before Blackburn, I enjoyed my football in Monaco - I played in the Champions League final - but my first three years in the Premier League with Blackburn were the best moments of my career.
"It was an amazing experience for me and one I will never forget. Blackburn Rovers will always have a big place in my heart and I am sad to be leaving, but last season was hard for me and I think it is better for me and my family to go back to France.
"But once again, I say thank you to the club for giving me a chance to play in England and thank you to the fans for your support - I will never forget it."
Bowyer added: "We're sad to see him leave, but he was eager to return to France and he wants to play more football at this stage in his career, which we fully understand, so I think this is the best solution for both parties."
- Sports & Recreation
- Blackburn Rovers
- Morten Gamst Pedersen
- Gary Bowyer