If you look at *hraigrō, you can see the /ai/ was still in flux during Old Dutch and Old French.
I know that PGm. *eu survived in some Frankish names as /eo/ or /ēo/, which might have sounded like [ɛːo]. I'll try and dig up a noun that made it to Old French.
Dutch is right on the border area between ē and ei. Most Dutch words have ē, but it seems that certain words, in particular those with umlaut, have ei instead. The words with ei become more frequent as you head east and south, and the form reger is also attested in Middle Dutch. With *hraigrō there is another explanation though: the -g- that disappeared may have raised the vowel before it. I think there are other words that have that (including native Romance ones).
uo doesn't stand for [øː] though, it stands for [uo]. uo developed in Old Dutch and Old High German from Proto-Germanic stressed ō in all words (OHG has guot for *gōdaz), and in a few also from wō (kuo (“cow”) < *kwō-, Old Dutch huo < *hwō). There is also a parallel change from ē to ie. I think the earliest Old High German texts have ua or oa, but most have uo. I think they also have ea and ia early on, and ie later. ( has ua and ia) So *muotan certainly came from *mōtan, not *mōtjan. But I'm not sure whether the change ō > oa/ua and ē > ea/ia happened already in Frankish.
Do you know if there is any evidence in Old French regarding this change? We know that Germanic au appears as ō, but what does Germanic ō appear as?
Well, if the same sound ends up in modern French as two different sounds, I wonder why that is. So I'd like to be able to compare other words that were borrowed from Germanic ō, to see if there is any general rule or pattern to them. And maybe through that, we can figure out whether Frankish still had ō, or whether it had already become a diphthong.
Frankish/Old Dutch th becomes d in (Middle) Dutch, so that can't be right. And Germanic eu becomes ie, not ū or ui, so that can't be right either.
I don't think that's right, either. Germanic *þeutōn would give *thiota in Old Dutch and *diozza in OHG, and the modern words would have been *diet(e) and *Dieß(e). Which is very different from the actually attested words. Dutch tuit can only go back to Germanic *tūt- or *tiuti-/tiutija-.
I can't actually find any sources about that. I've found vlieke in a Middle Dutch dictionary, but that says it was borrowed from French rather than the other way around. The combination of -iu- and -kk- also bothers me. Normally -kk- is formed from -k- followed by -j- through gemination, but that only applies to light syllables and the -iu- makes it heavy. So it seems that the Germanic form must have been *fliukkijōn. I have no idea how that could have become the Middle Dutch word, though; the -kk- should have been preserved and -iu- normally becomes -u- in Middle Dutch, only -ie- in a few dialects. So maybe it was really *fliukijōn or even *fleukōn.
In any case, I don't think the evidence for this reconstruction is strong enough to warrant an entry. I'd prefer it be deleted.
You're right, looks like Du. vliek is actually a reconstruction from OFr., but it does have obvious Frankish origins, with many cognates, so it shouldn't be outlandish to reconstruct. http://gtb.inl.nl/iWDB/search?actie=article&wdb=ONW&id=ID3683&lemmodern=vliek