19 of the Russian's twenty-one championships have been earned on hard surfaces
A revitalized Medvedev won his maiden championship for 882 days with success over opponent Moutet in the Almaty Open title decider.
Medvedev, a former number one, has experienced a challenging period, achieving just a single victory at the big events and suffering a difficult moment at the US Open.
Medvedev's varied form on the professional circuit - and difficulties with his service game in especial - resulted in him exiting of the elite rankings and eventually splitting with long-term trainer Gilles Cervara.
Currently working with his coach and Goetzke, the tennis star has steadily progressed in the recent weeks - climaxing in a tightly fought competitive victory over opponent Moutet.
This represents his initial championship since the Italian tournament and first on a hard surface from March of the previous year.
Success also indicates Medvedev has won 21 championships at 21 distinct competitions.
"This marks the first occasion I am participating in a tournament with my both daughters simultaneously, so to get a trophy is particularly special," stated ranked player Medvedev.
"This title is in dedication of my child Victoria, because the initial championship I got when my first daughter my daughter was born was for her."
The athlete, the former major winner, had lost his past six finals, including in the German tournament earlier this year.
The player's retrieving strategy and regular emotional displays on court had led commentators to doubt if his skill to perform at the elite level was finished.
But the 29-year-old has altered his approach in the past month, attempting to come to the net and compete aggressively, supported by an better service.
Medvedev came back from a disadvantage in the first set against the challenging opponent, winning 4 of the concluding five exchanges to take the lead.
Both players exchanged service breaks in the middle set before the Frenchman, bidding for his initial ATP Tour title, gained dominance to push for a decider.
Moutet defended 4 early-game chances in a close deciding set before Medvedev won the break to that score to serve for the match.
Suitably, the winner earned the win with a point at the net area, with Moutet failing to control a volley after over two and a half hours.