... seems an important quation is somewhat forgotten atm in this discussion:
How Petain IOTL actually came into his position and who should have replaced him in that.
IOTL he was 'asked' to enter the french goverment and did so as Deputy Prime Minister on 18th May.
Well before 'Dunkirk) and 'Case Red' beginning.
With his insistance for seeking armistice even before him being made head of the goverment on 16th June he was rather instrumental for this actually happen - both him becomming Prime Minister and armistice.
With him NOT in place IMHO there are quite good chances, that the french goverment flees and set up itself in exile or in a Bretagne redout or in North Africa become very likely.
If there would than be a French Goverment at Vichy at all ... this time with very much less legitimation and this time a truly 'only puppet' by german making.