His time of 48.77 seconds narrowly edged out Marco Di Carli of Italy, who clocked a time of 48.81.
Leveaux had to settle for second best in the 200m freestyle on Wednesday, with German Paul Biedermann storming to his second gold of the championships.
But the French swimmer is determined to make amends over his preferred distance, and laid a marker down as he qualified for the semi-finals.
Romanian Norbert Trandafir set the third fastest time of 49.09.
Elsewhere, Ilaria Bianchi recorded the best time in the women's 100m butterfly heats, her 58.31 coming in precisely one tenth of a second faster than Norwegian Ingvild Snildal.
And Ireland qualified for the semi-finals of the women's 200m freestyle relay with the seventh best time of the morning session.
Their combined total of eight minutes and 13.30 seconds was 7.47 behind fastest quartet Hungary, with Slovenia and Spain rounding out the top three.
- Sports & Recreation
- Swimming & Diving