The are a lot variables between the the Battle of France and the Battle of Britain including perhaps pilot experience/training and average height of combat.
Both the British and French air forces were expanding tremendously in late 30s and a lot of the pilots are going to be low time ones. Perhaps the French pilots got better gunnery training? Perhaps the Hawks had their guns all pointed in the same direction?
The Germans were flying a lot more low level missions in support of the ground troops in France and their fighters may have been a lower levels. the low altitude engines of the Hawks (and the two speed Cyclone wasn't any lower than the DB601) may not have been a large disadvantage in France. I have not seen a breakdown of the claims of the French Hawks, as in how many 109s, how many He 111s, how many Ju 87s how many Fi 126s etc.
Expecting the Hawk to do as well over England where, in general, the altitudes were higher and their were fewer 'tactical' aircraft flying may be a different story.