19 of the Russian's twenty-one titles have been earned on hard courts
A resurgent Medvedev won his first title for 882 days with victory over opponent Moutet in the Almaty Open title decider.
The athlete, a former world number one, has experienced a torrid season, achieving just one match at the big events and suffering a difficult moment at the American major.
The player's unpredictability on the ATP Tour - and difficulties with his serving in specific - resulted in him falling of the top ten and finally parting ways with long-term mentor Gilles Cervara.
Now working with his coach and Goetzke, the tennis star has gradually progressed in the last few weeks - climaxing in a closely contested 7-5 4-6 6-3 victory over Frenchman Moutet.
This marks the player's first trophy since the Italian tournament and maiden on a hard court after spring of 2023.
Victory also indicates the Russian has secured 21 titles at 21 distinct competitions.
"It's the first time I'm at a competition with my children simultaneously, so to win a trophy is really nice," stated world number 14 the champion.
"This championship is in honour of my second daughter my daughter, because the first title I got when my child Alisa was born was for her."
The tennis star, the 2021 US Open champion, had lost his last six finals, including in Halle previously this season.
His defensive approach and recurring reactions on court had led observers to doubt if his capacity to play at the elite level was concluded.
But the player has altered his approach in recent weeks, attempting to come to the net and play positively, supported by an improved serving game.
The champion fought back from a break down in the opening set against the tricky Moutet, taking four of the final five games to take the lead.
The pair exchanged break points in the middle set before the Frenchman, striving for his maiden ATP Tour victory, seized the initiative to push for a third set.
He rescued 4 initial chances in a tight deciding set before the Russian secured a break to 15 to close out the victory.
Appropriately, he clinched the title with a rally at the front of the court, with his opponent incapable to handle a shot after over two and a half hours.