So to continue the thought experiment here a bit, to it's logical conclusion...
If, let's say, France somehow survived the initial onslaught by whatever means you want to think of, and achieved a kind of stalemate for lets say six months,
you will have by then very competitive fighters, arguably, such as VG 39bis and D.524 and probably MS 540 too. MS 406 was actually a pretty agile fighter and did well for the Finns, it was just too slow. The 540, VG 39 and D.524 are all going to be in the 360-390 mph range, they are all agile with fairly low wing loading, climb pretty well, have armor and self sealing fuel tanks, have decent range, and good to very good armament. 20mm hub cannon is a lethal weapon for air to air combat. Later versions of these fighters also had two 20mm wing guns so that becomes heavy firepower indeed.
Arsenal VG 39 - 388 mph at 5800 m / 19k ', range 750 miles, armament 1 x 20mm 4 x 7.5mm machine guns, wing loading 36 lbs/sq ft (HS 12Y-51 Engine)
Arsenal VG 39bis - 418 mph* at 7000 m /22k ' (military power) 446 mph* (WEP), armament 3 x 20mm machine guns (HS 12Z-17 Engine)
Dewoitine D.524 - 382 mph* range 780 miles, wing loading 34 lbs / sq ft, armament 1 x 20mm and 4 x 7.5mm machine guns (HS 12Z-89ter Engine)
Morane MS 540 - 391 mph, range 400 miles, wing loading 19 lbs / sq ft, armament 1 x 20mm 4 x 7.5mm machine guns (YS-2 engine, Doflug 3802 numbers)
Climb rates for all three seem to be around 2800 fpm initial for the early / 1940 version (no improved engines) a bit over 3,000 fpm initial for the bigger engines.
And let's not forget the
LeO 451 bomber (308 mph, 1800 mile range and 3400 lb max bomb load, and 20mm defensive gun in 1940), the
Breguet 693 attack plane (300 mph, 840 mile range, 20mm cannon armed, in 1940), and
Bloch MB 174 recon plane (330 mph, 290 mph cruise speed, 1000 mile range in 1940)**
We can also add to this a larger number of P-36 / Hawk 75 (the most successful fighter for the French during the actual Battle of France), probably early P-40 / Tomahawk type fighters, with improved Tomahawk and maybe P-40D / Kittyhawk type by
maybe mid 1941, plus early Martlet / Wildcat fighters (Grumman G-36); A-20 Boston (340 mph),
Martin 167 Maryland (300 mph, 1,200 lbs bombs and 1300 mile range) and Martin 187 Baltimore (300 mph, 2,000 lbs bombs,, 980 mile range) type fast bombers, SBD dive bombers (as we know, accurate but vulnerable), maybe even a few early P-38s. All of this gives them some Tactical and Operational striking power. The French may have had some other important US or British types on order that I forgot or wasn't aware of.
Plus the British will almost certainly be helping with their Spit Mk I and II, Hurricane Mk 1 and II, and eventually also Spit Mk V. Maybe a few Whirlwinds and Beaufighters. Probably night and maritime raids by their heavy / long range bombers.
Now the big weakness with these all fighters is that none of them had two speed or two stage (or turbo) superchargers. Even the P-38s, if any arrived, would be the pre-turbo types. So they are going to be limited at altitude. If the (extended) Battle of France is going to be a Battle of Britain redux, that would be a problem.
But I would argue that it wasn't going to be that, because it was also going to be a ground war. And (again, arguably) the greatest offensive strength for the Germans in the ground war was the Ju-87 dive bomber. The Ju 87 was key to their victories at Arras etc. So I think this would much more closely resemble the Desert War in North Africa. Only in this scenario (Battle of France late 1940 / and into 1941) the French here have much more competitive fighters. All of these fighters listed above could compete with the best German fighters of 1941, the Bf 109E and Bf 109F. The Bf 109s have two advantages here, climb rate and altitude capability. Meaning they will often be attacking from above. On the other hand, they'll be at a disadvantage in a dogfight. The British were able to compete with these successfully in North Africa, once they made some tactical adjustments, using mainly Kittyhawks Mk1 and Hurricane IIs, by mid 1942. Arguably a VG 39bis or Dewoitine 524 is a bit more competitive against a Bf 109F, though the French would need to be able to adjust their tactics successfully. They did for example have a good bit higher performance ceilings than an early Kittyhawk.
Which they apparently did already do in the actual Battle of France with their Hawk 75s.
The French fighters, or two of them, also have range more like the Kittyhawk did in North Africa, meaning they could escort some of their best available fast bombers on not just Tactical but also Operational strikes like against supplies, airfields, depots, railheads, bridges etc. etc. They could also use Kittyhawks, if they got any, as pretty effective dive bombers.
Then the next question mark for me comes in with the arrival of the Fw 190. Can any of these French fighters compete? Probably the Arsenal V.39bis can, but it's going to need a working HS 12Z engine. That's unclear both for "if" and "when".
I would say that in some scenario where they had a few more months, the French
should have been able to neutralize the huge asset that the Ju-87 was for the Germans, much as it was neutralized in North Africa, and they would have been able to start hitting the Germans both in the battle and behind their lines, as was also done with success in the Desert War.
* These are estimated speeds, the others are tested speeds
** All three of these are the
unimproved versions. All could and likely would have got more powerful engines by 1941.