Perhaps the Germans plan to to use the V1 as a terror weapon against Paris. They want to compliment the effects on the civilian populations, learned in Poland, with the Stuka. However the rapid fall of France short circuits those plans.
Also remember not to think of the V1 in terms of OTL. Think in terms of a 1940 deployment as per the OP. In 1940 a “robotic” 400mph flying bomb, is right out of Buck Rodgers.
So…………On the heels of the fall of France and the evacuation of the BEF, the Chain Home stations begin to pick up very small/very fast targets coming over the channel at night. As a result, defense is VERY difficult, with luck being the most plausible. Stuka sirens have been fitted to the V1, triggered to start wailing when the V1 begins its dive. So the residents of London first hear the distinctive sound of the pulse jet, followed by a terrifying howling, and ending in a massive explosion. These attacks signal the beginning of,and continue throughout, the BoB. Luftwaffe and sporadic V1 attacks during the day, plus the V1s attacks at night. Meanwhile the V1 launch sites are surrounded by heavy flak and fighter defenses, hoping the RAF sends planes/crews to attack them.
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