From what I understand, the Germanic tribes borrowed their calendar and names for days of the week from the Romans. But they decided to localize the gods - Thor's day, Frey's day, etc. How come the months didn't get the same treatment, and are still named after Octavius, Augustus, Julius, etc?
Bede mentioned the month-names the Old English used for their lunisolar calendar, and they are indeed quite different. For instance, December and January were basically called "Before Yule" and "After Yule", while June and July were "before midsummer" and "after midsummer". Old English also had a name for the leap month occasionally required to realign the lunar calendar with the solar cycle.
I can (and at one point did) give a lot of speculative reasons for why those names were abandoned. All we can say for sure is that the two calendar systems are a bit different (due to the use of leap-month rather than leap days), and when the English shifted to using the Julian one instead they decided to use its names as well, rather than try to map them to onto their old calendar names.
However, this didn't happen everywhere. Charlemagne came up with his own month names, that survived in some places on the continent until the 15th century. Either the (likely Norman) rulers of England didn't do the same thing, or whatever they tried didn't stick.
Why didn't the same thing happen with the days of the week? The only factual info I can give is that the borrowing of the concept of numbering/naming the days of the week came much earlier; around the first century.