Nineteen of Medvedev's 21 championships have been achieved on hard surfaces
A revitalized the Russian player secured his initial championship for 882 days with a win over opponent Moutet in the Almaty Open title decider.
Medvedev, a former world number one, has endured a torrid season, achieving just a single victory at the major tournaments and undergoing a difficult moment at the New York tournament.
Medvedev's varied form on the ATP Tour - and issues with his service game in specific - led to him falling of the world's top 10 and finally splitting with long-term trainer Gilles Cervara.
Now collaborating with Johansson and Goetzke, the tennis star has consistently improved in the last few weeks - peaking in a tightly fought 7-5 4-6 6-3 win over opponent Moutet.
This marks Medvedev's first championship following the 2023 Rome Masters and initial on a hardcourt since March of the previous year.
Victory also indicates the Russian has achieved 21 championships at twenty-one various events.
"This marks the first occasion I'm at a competition with my children at once, so to get a championship is really nice," commented ranked player Medvedev.
"This title is in honour of my second daughter her name, because the maiden victory I achieved when my older daughter her name was delivered was for her."
The athlete, the 2021 US Open champion, had lost his past six finals, comprising in Halle earlier this year.
The player's counter-punching play style and frequent reactions on court had caused some to question if his ability to play at the top level was finished.
However the 29-year-old has made changes in the last few weeks, attempting to come to the net and perform assertively, backed up by an enhanced serving game.
Medvedev fought back from a disadvantage in the initial set against the tricky Frenchman, winning four of the last five games to take the lead.
The pair traded service breaks in the following set before the Frenchman, bidding for his maiden tour championship, took control to push for a final set.
The opponent saved four initial chances in a tight third set before Medvedev won the break to fifteen to secure the win.
Suitably, he earned the title with a rally at the front of the court, with Moutet unable to handle a volley after over two and a half hours.
