After a tight opening to the match, Metz were the first to take a two-goal lead, as they led 7-5 after 16 minutes.
The 20-year-old Lylou Borg showed her talent in attack, combining well with Sarah Bouktit, and their impact helped the French side extend the gap to 11-7 and the home side maintained a four-goal advantage at half-time.
While Esbjerg's Henny Reistad seemed to lack her usual focus and was guilty of missing several chances, Metz were more clinical in their attacking moves and continued to increase the gap after the break, capitalising on Esbjerg's multiple mistakes.
Their goalkeeper Johanna Bundsen also did a good job, finishing the game with 15 saves and a 38 per cent save rate.
With 10 minutes remaining, Lucie Granier handed the French side a double-digit lead, 31:21, and Metz ultimately hit the 40-goal mark, clinching a big win.