Fledgling Eagles is very good I think, very detailed (Armée de l'Air and RAF). It had 5 authors including Christopher Shores, who publishd an English edition. I think there is a more recent one in English (?). I was under the impression that the original question was aimed at May-June 1940 (French Campaign).

One of the French "classics" is "Ils ouvrirent le bal" (They opened the dancing), published 1967 by Jean Gisclon, who was a sergent and a fighter pilot about 1936-45, 1939-40 with GC II/5 flying Curtiss H-75s. I discovered it... in a bookshop in Nürnberg (!) - I was living 10 miles from this city - for it was translated into German, a very exceptional honour for a French aviation book. Exceptionally the translation seems to be accurate except when there were accusations, aimed at German pilots, of having shot parachuted aircrew. It covers French fighters only and their combat, 1939-40, on a chronological basis. It is fairly accurate but contains many errors in details (for ex. some pilot names, killed or not...) too. As a whole it brought a lot of hitherto unknown information on French losses but also on very numerous victories, most of which hardly can be disputed at all. This book has the undertitle "Les mille victoires de la Chasse française", "The 1,000 victories of the French fighter arm". This figure was widely accepted in France for a number of years although 919 is more accurate, including September 1939-May 1940. Gisclon obviously teared and stretched the figures in order to reach the magic figure of 1,000 (1,006 to be accurate, I think). Now there is a big controversy about it in France, some French people trying to ridicule it with the greatest energy. Personally I NEVER supported the figure of 1,000 victories - up till now. Some years later Gisclon published "La grande aventure de la Chasse française 1939-1945", a big heavy thing, and more recently, around 2000, a new book : "Les mille victoires de la Chasse française", which I haven't read for I assumed it would be much the same as his first book. It should be noted that Gisclon is a member of the by far much more numerous French community which all the time will cry, wail and lament that we suffered soooo terrible losses and had got virtually nothing, only our guts, to fight "15,500" German aircraft, etc. A typical example in Gisclon's books could read as follows : "9 Curtiss fighters (often it was 27) take off towards the front zone. They meet 300 German bombers escorted by 50 (or 40 or 200 etc.) Me 109s" (these are typical figures in FRENCH reports; often the proportions are reversed in German stories, where 4 French fighters used to attack one bomber and a JG 3 Gruppe (I. I think) reported that French fighters almost invariably had a heavy numerical superiority. This seems to be a matter of point of view.) "In the ensuing fight they manage to shoot down (here he gives more details) 3 bombers and 4 of the escorting fighters. But alas these victories are dearly paid for, oooooh, how terrible, wail, cry, sob, Lt. Dupont is killed and Sgt. Durand is wounded in his leg." Such people do not accept ANY losses at all. I agree that every loss was one loss too many, every aircrew killed hurts still today, but I know that you can't go to war and expect nil losses. In fact French losses (at least in air combat, excluding Flak) were very reasonable and after the armistice the whole French Air Force had not at all the impression of having been wiped out or beaten, ON THE CONTRARY. They felt they had won and rightly so. Won the air war of course not the campaign as a whole.
For my part I have been fighting this unjustified book and magazine pessimism for 15 years, starting with the book (my title!) "Invisibles vainqueurs", the official author of which was Paul Martin. I contributed half the book and numerous corrections but I couldn't print my name both as publisher and as co-author : the silly French booksellers would have refused to sell the book. I discovered too late that Martin was interested in, and reported, French LOSSES only except in a few tables. Losses did exist but they were less than half the story! In my eyes this was a disaster, which is why I added hundreds of "optimistic" pages in compensation. The result was a rather strange book.
1999 or 2000 "Jacqueline and" Paul Martin published the same stuff again under the title "Ils étaient là...", heavily stressing French losses again, victories being very "small", mainly in a few tables. Publisher C-J Ehrengardt was forced, he too, to add many explanations and comments but he belongs to the "pessimists" about the Armée de l'Air so what he wrote fits much better into Martin's long, dire list of dead airmen and destroyed French aircraft. If you're looking for exact AC serials, aircrew names or names of villages etc. this is a good source.