During the summer transfer window, the defender was one of more than 20 players to make the switch to the City Ground after Forest's promotion to the Premier League.
On the back of making 33 appearances for Troyes in Ligue 1 last season, the 22-year-old had been expected to earn regular game at the East Midlands outfit.
However, Biancone has instead been limited to just 16 minutes of action in the top flight, making substitute outings against Manchester City and Brighton & Hove Albion.
Those appearances came after Biancone had initially played the full 90 minutes during a 3-0 triumph over Grimsby Town in the EFL Cup.
Nevertheless, the former France Under-19 international will play no further part of the 2022-23 campaign after sustaining an ACL injury in training.
Speaking to reporters at a press conference, Cooper said: "It's really difficult news for him and a blow for us because although he hasn't featured too much, he was making good progress and is a player we really like.
"We're gutted for him because it's a serious one and it's a blow to the group."
Although Forest are well stocked for options to cover for Biancone's absence, the summer arrival had been capable of deputising across the entire backline.
While his one start came on the right-hand side of a back three in a game where he also captained the side, he has also featured at right-back and left-back during his career.
Neco Williams and Serge Aurier will now continue to compete for the right wing-back role, with Renan Lodi and Harry Toffolo fighting for the position on the opposite flank.