Nineteen of Medvedev's twenty-one titles have been earned on hard surfaces
A comeback the Russian player secured his initial championship for nearly 30 months with victory over opponent Moutet in the tournament title decider.
The athlete, a former top-ranked player, has experienced a difficult year, managing just a single victory at the major tournaments and experiencing a difficult moment at the New York tournament.
Medvedev's unpredictability on the professional circuit - and difficulties with his serve in specific - resulted in him exiting of the elite rankings and ultimately parting ways with long-time trainer his previous coach.
Now working with Thomas Johansson and Goetzke, Medvedev has steadily progressed in the past month - climaxing in a closely contested 7-5 4-6 6-3 win over challenger Corentin Moutet.
It is the player's initial championship following the Italian tournament and maiden on a hard surface from March of that year.
Success also means Medvedev has won twenty-one titles at 21 distinct competitions.
"For the first time I have attended a event with my children at once, so to win a title is particularly special," said world number 14 the champion.
"This title is in tribute of my child her name, because the first title I got when my child her name was delivered was for her."
Medvedev, the former major winner, had failed in his last six finals, including in that event earlier this year.
His retrieving approach and recurring reactions on court had caused observers to doubt if his skill to compete at the top level was concluded.
Yet the player has made changes in the past month, attempting to advance forward and play assertively, reinforced by an improved serving game.
He fought back from a deficit in the initial set against the challenging opponent, taking 4 of the concluding five exchanges to go ahead.
Both players swapped breaks in the following set before the Frenchman, attempting for his maiden ATP Tour championship, took control to create a final set.
Moutet saved 4 early-game chances in a close deciding set before Medvedev broke to that score to secure the win.
Suitably, Medvedev earned victory with a shot at the net area, with the Frenchman incapable to control a shot after two hours and 38 minutes.
