The company said the group overall - comprising the networks of Air France KLM, Hop! and Transavia - carried 9.3 million passengers in June, up 3.7 percent from a year earlier.
The overall load factor, a measure of the extent to which an airline has filled its planes, rose to 89.3 percent in June from 87.7 percent last year, it said.
The higher figures lifted Air France KLM shares, which were up 7.2 percent in mid-session trading, but they remain down by roughly 40 percent so far in 2018, mainly due to the impact of the strikes on the company.
"Overall, June's traffic stats are a return to normality and highlight the favourable market conditions that exist despite the strike which impacted April and May results," wrote Irish brokerage Goodbody in a research note.
"Discussions on a new CEO continue and this appointment will be crucial for further union negotiations over the summer/Q3 period," added Goodbody.
Air France KLM said last month it hoped to appoint a new CEO "as quickly as possible", against the backdrop of concerns by some shareholders about the process.
The airline has been hunting for a new boss since the abrupt departure of Jean-Marc Janaillac in May after staff rejected a pay proposal aimed at ending a series of strikes that have led to heavy losses.
French newspaper Le Figaro reported on Monday that Catherine Guillouard, chief executive of French public transport group RATP, was being considered for the Air France KLM CEO position.
An Air France KLM spokeswoman declined to comment.
Last week, France's transport minister Elisabeth Borne said it was important the new CEO was an air transport specialist.
The French government has a stake of about 14 percent in Air France KLM.
Delta Airlines and China Eastern Airlines each hold 8.8 percent, while Accor has considered taking a minority stake in Air France KLM to help Accor compete with broader travel packages offered by online rivals such as Expedia and Booking.com.
Brokerage Goodbody said Guillouard could be a solid appointment, given her experience dealing with transport unions, including those at Air France.
But two sources told Reuters she was not an official candidate.
"She is not a candidate, no! But as her CV ticks a lot of the right boxes, people are thinking about her. A lot of people would like her to take up the job," said one source.
A third source said it would be hard for the government to back Guillouard, as it would leave a gap at the RATP, with Guillouard having only taken over at the RATP a year ago.
Recruitment firm Egon Zehnder is helping out in the search for a new Air France KLM CEO.
(Reporting by Sudip Kar-Gupta; Additional reporting by Gwenaelle Barzic and Jean-Baptiste Vey; Editing by Mark Potter and Edmund Blair)
By Sudip Kar-Gupta and Jean-Michel Belot