Did OE have progressive aspect? Did it enter the language with the French after the Norman Invasion?
Modern High German has no progressive aspect, but often in spoken German activities in progress are described by using "beim" + V INF, and infinitive verbs in German typically end with -en. Is this possibly the origin of our progressive aspect form? I may be going out on a limb here with my wild conjecture, but the German PREP "bei" looks a lot like the progressive AUX "be", and the -en infinitive is awfully similar to the English present participle -ing.
The OED says "be" comes from OHG "beom" = Eng "become", and the prefix be- is still very common in MHG, usually meaning to have someting done to the subject as in passive voice (e.g. begrenzen). This is still occasionally seen in Modern English verbs like "befriend".
Could it be that AUX "be" comes from "bei" and because of its similarity transformed into "be" in a similar way to "God" changing to "good" in "good bye" (orig. "God be with you")?