Might be worth my while following this book up.
Ok, I did some more research (including purchasing the book in question and reading the section on AIM-9C right away). Quite interesting in that it speaks highly of the AIM-9C development. There is no real talk of poor performance in regard to the radar - in fact, the author (and the guys at the time) speak quite highly of the F8U-2NE Crusader's Magnavox AN/APQ-94 whereas they were far from impressed with the Westinghouse AN/APQ-72 in the F-4Bs at the same time. The basic summation was that the F-8/APQ-94/AIM-9C combination worked quite well (for its day) and that the only reason the AIM-9C was eventually withdrawn was that the F-8 was also being withdrawn. They did say that pilots were at first sceptical of the AIM-9C's SARH guidance and the fact that they would be able to use it as an all aspect weapon (i.e. no longer be forced to only fire in a tail chase scenario, which was typical of the IR guided AIM-9B/D) but that this was overcome once they saw it operate. I wonder if this doubt is still part of the lingering misinformation about the weapon? I also suspect that the limited production numbers were still tied to my previous comments about minimal use of such weapons due to engagement parameters, including the fact that the IR guided versions were fire&forget whereas the SARH version required the pilot to keep pointing towards the target?
Either way, I think the AIM-9C is still a useful weapon (for its day) and there is certainly no mention of doppler radar, or lack thereof, issues. That said, the system was certainly not 'look down-shoot down). In fact, no-one had this capability operationally until the F-4J/Westinghouse AN/AWG-10 combination in the late 1960's/early 1970's ( I was wrong with the F-15 comment earlier). Therefore, I wouldn't really hold this against the F-8/AIM-9C.
That said, giving the Mirage with its Cyrano II radar the AIM-9C may have issues. For one, there would need to be some compatibility matching though this is not impossible to overcome - after all, the Cyrano was able to guide R.530s which were also used on Aéronavale F-8E(FN)s. One issue
might be the dish diameter (this was something mentioned in the Sidewinder book) with the Cyrano II having a dish of 36cm whereas the AN/APQ-94 was of 53.3cm (21"). One option
might be to try to give the Mirage III the AN/APQ-94 and possibly result in a 'big nose' Mirage (the "Cyrano de Bergerac" version?).