Just at the start of CRUSADER, Flight published an interesting article on the Free French Air Force, with some interesting pictures (if anyone can tell me what kind of a plane General Valin is standing in front of, I’d be grateful – I thought it was a Bf 108, but it has a fixed undercarriage, so that can’t be it). The article can be found at this link. The Flightglobal archive is generally very interesting, by the way.
The major contribution by the Free French to the battle was the 1st Bombing Group, known as the Lorraine squadron, a Bristol Blenheim equipped light bomber squadron consisting of two flights. In the course of operations, it lost 1/3rd of its flying personnel killed, missing or wounded, including its newly arrived commander in December, Lt.Col. Pijeaud, killed on his first mission when his plane was attacked by Axis fighters. After the withdrawal of Axis forces to the west, the Group remained on the Egyptian border, based on Gambut airfield. After helping the Axis on the way by bombing rear area installations such as El Magrun airfield halfway between Benghazi and Agedabia (see below), it engaged in the bombardment of the Axis border fortifications of Bardia and Halfaya (see this older post). In the middle of January 1942 it was withdrawn for refitting to Syria. During the 16 days before the surrender of the Halfaya garrison, the Lorraine flew 300 sorties against it, from Gambut airfield. In fact, together with other light bomber units the amount of sorties climbed to a level prompting inquiries from Whitehall if this was really necessary!
This French language site has some good information on the unit, including pictures. At this link you can find a nice colour profile of a Bristol Blenheim Mk.IV in Free French colours. Just ignore the statement that they were operating in the Western Desert in February 1942. Funnily enough, it appears Airfix (ah, bane of my youth) also did a kit of the Lorraine Blenheim (apparently its a good kit too – check the link through the picture below).
Towards the end of the CRUSADER battles, the Free French 1st Fighter Group Alsace started operations in the air defense of Egypt, based at Ismailia on the Suez Canal, having just been re-equipped with Hurricane I fighters. Some information on this can be found at this link.
A lot of good information about Free French forces in North Africa can be found at this link.