The Danish World No. 3 played a great final throughout but in the end, but in the end struggled with his physique.
Antonsen was clearly hampered in his movement, but fought fiercely and took down the French home court hero, No. 8 in the world, winning 21-12, 21-19.
The French tournament is ranked at the same level as the Denmark Open. Excluding the season finale, the level is just below the four biggest tournaments on the BWF World Tour.
Anders Antonsen got off to a flying start in the final of the French Open. The Dane was convincing and quickly took a comfortable lead in the first set and never looked back to win 21-12 on his first out of ten set points.
The French home court hero worked his way into the match and narrowly took the lead in the second set after sublime net play followed by a resolute smash into the body of Antonsen.
As so many times before, the Dane showed great character and once again turned the match in his own favour.
The Dane was on course for victory with a lead of 16-12, but Popov managed to restore parity against a physically exhausted Antonsen, who still had air to win the final points.
Towards the end, it was visible that Antonsen had been through some tough matches on his way to Sunday's final.
The semi-final featured more than 90 minutes of badminton in a grueling match against China's Li Shi Feng.
Countryman Viktor Axelsen was eliminated in the quarter-finals, which also had to be decided in three long sets.