Martinot-Lagarde, in 13.14 for his 12th international medal, and Kwaou-Mathey, in 13.33 for his first, were dominated by the Spaniard Asier Martinez, separated by a thousandth of a second with "PML".
The third Frenchman qualified for the final, Sasha Zhoya, fell and finished 8th and last.
At the end of a suspenseful final, Martinot-Lagarde, defending champion, almost overtook "broken" Martinez (22 years old).
But it was ultimately the Spaniard, bronze medalist at the Worlds last month in Eugene (United States), who was proclaimed winner by a thousandth of a second.
The 30-year-old Frenchman once again concluded with a championship medal a season marred by several injuries and setbacks, which may have explained his elimination in the semi-finals in the United States last month.
Just Kwaou-Mathey is only 22 years old.
And his bronze medal rewards the progress of the man who has become a reference in the discipline this year.
Great hope of tricolor athletics, Zhoya for his part fell at the end of the race when he did not seem able to play for a medal.
It was his first final after his first season as a senior.
© 2022 AFP