In general you will find the cheapest flights from May to middle of June and September to end of November 2018. In some cases (e.g. to the Caribbean destinations) also in first quarter of 2019. Anyway travel dates vary by each of the selected destination. I recommend to follow below link where you can easily compare all the cheapest flights. Simply choose your desired destination and click on follow. Air France will conveniently offer low-cost calendar by each month. Validity of this promotion vary by chosen destinations. Some of the cheapest seats are available till 12th of April but few deals till 16th of April.
Paris – Cincinnati from €394 (6. – 19.5.)
Paris – Seattle from €395 (13. – 20.5.)
Paris – Chennai, India from €412 (operated by Jet Airways)
Paris – Beijing from €462 (23.9. – 2.10.)
Paris – Guadeloupe from €349 (28.1. – 4.2.2019)
Paris – Martinique from €349 (12. – 26.11.)
Paris – Havana, Cuba from €499 (21. – 28.5.)
Paris – Johannesburg from €513 (13. – 20.5.)
Booking sample of special sale of a SkyTeam carrier. Air France cheap non-stop flights Paris to Seattle, Cincinnati, Nairobi or Beijing from €394! also as per our above booking sample your outbound flight from Paris Charles de Gaulle to Seattle would be on Sunday, 13th of May. Your inbound flight from North America back to France then a week later on 20th of May 2018.