19 of the Russian's twenty-one victories have been won on hardcourt
A comeback Medvedev won his first title for over two years with a win over opponent Moutet in the competition title decider.
The Russian, a ex- number one, has experienced a torrid season, achieving just one match at the big events and suffering a setback at the US Open.
Medvedev's varied form on the ATP Tour - and difficulties with his serve in specific - caused him exiting of the elite rankings and eventually separating with former trainer Gilles Cervara.
Now collaborating with Thomas Johansson and Goetzke, he has gradually advanced in the last few weeks - culminating in a closely contested 7-5 4-6 6-3 triumph over opponent Moutet.
This marks Medvedev's first championship after the 2023 Rome Masters and maiden on a hardcourt since March of the previous year.
Victory also indicates he has secured twenty-one titles at twenty-one distinct competitions.
"This marks the first occasion I'm at a event with my both daughters together, so to secure a trophy is particularly special," stated world number 14 the champion.
"This title is in dedication of my child my daughter, because the maiden victory I achieved when my older daughter Alisa was delivered was for her."
Medvedev, the former major winner, had lost his previous six title deciders, featuring in Halle in the past months.
The player's counter-punching play style and regular reactions on the tennis court had caused some to question if his skill to perform at the elite level was finished.
Yet the player has implemented adjustments in the last few weeks, striving to advance forward and compete aggressively, supported by an enhanced service.
Medvedev recovered from a break down in the first set against the challenging opponent, securing four of the last five games to gain the advantage.
The competitors traded service breaks in the second set before Moutet, bidding for his first ATP Tour championship, gained dominance to force a third set.
Moutet rescued 4 early opportunities in a tight final set before Medvedev secured a break to that score to secure the win.
Appropriately, Medvedev secured the title with a point at the net area, with the Frenchman unable to manage a return after a lengthy match.