Air France saw its passenger traffic increase 4.6 percent in June, while cargo traffic fell 2.8 percent, the company said in a statement.
Passenger traffic grew most strongly in Asia where comparisons were easier because of the impact of the tsunami last year on travel, and US and Africa and Middle East traffic also progressed.
Cargo traffic was hurt by the degradation of the economy, although performance improved in recent months.
"Capacity was reduced by 1.4 percent while cargo traffic declined by 2.8 percent," said Air France.
The Paris-based airline will publish first-half results on July 30.