Monaco held on for a 2-0 victory over Amiens, who entered the match one spot ahead of the principality club in 18th place.
With the victory, Monaco leapfrog Amiens and Dijon on goal differential, temporarily moving into a safe spot in Ligue 1.
Now in Week 16 of the Ligue 1 campaign, it's the first time the club has escaped the drop zone since Week 6.
The first goal came in the 46th minute of Tuesday's clash at Amiens' Stade de la Licorne, with Radamel Falcao providing the game-winner from the penalty spot.
Falcao added another from the spot in the 97th minute, capping the win after Amiens' Bakaye Dibassy was sent off in stoppage time.
The Colombian star now has seven goals and one assist on the season, with his goalscoring mark leading the club.
In total, Falcao has contributed to exactly half of Monaco's 16 Ligue 1 goals on the season.
Henry, who played for the club from 1994 to 1999, took charge in October following the dismissal of Leonardo Jardim.
The club were in 18th at the time of Jardim's departure, but Henry also endured a rough start that saw Monaco unable to secure a win for more than a month.