Air France expects to operate 42% of its flights today (Thursday) after estimating that 60% of its pilots plan to strike.
It says 7,000 other Air France employees are doing all they can to assist customers.
But it said customers with a flight reservation between 15 and 22 September are being encouraged to postpone their trip or change their ticket at no extra cost.
"Since last week, close to 1.1 million texts and messages have been sent to inform customers due to travel between 15 and 22 September, individually and in real time," it said.
"If the strike action continues beyond 18 September, the flight schedule will be adjusted accordingly. Customers will be informed of the potential impact the day before departure. However there may be other disruption and delays."
The SNPL union, which represents a majority of Air France pilots, has called the week-long strike as part of a dispute with the company over its strategy to compete against European low-cost rivals.
