United will face Newcastle in the showpiece on February 26.
Kylian Mbappe sparked fears over his fitness after limping off against Montpellier, but Christophe Galtier eased those concerns.
Bayern Munich collected their first win of 2023 with a crushing victory over Mainz as Joao Cancelo made his debut on Wednesday.
Manchester United have had to cope without Jadon Sancho and Anthony Martial, but the pair returned for the win against Nottingham Forest.