Bell Beaker is some 2,000 years earlier than Saxons, Franks or Frisians, and these later Germanic tribes are also more recent than most Belgae tribes, which were apparently absorbed during the Germanic expansion coming southwards from Jutland and Scandinavia. So, I think your question conflates many different chronological periods and also assumes that those were necessarily different peoples in terms of their main genetic makeup, which is definitely not a reliably established fact.
It is perfectly possible, perhaps even llikely, that the Belgians are still closely related to Bell Beaker in Belgium or neighboring areas AND ALSO to Belgae tribes AND ALSO to Franks inhabiting the area during the Middle Ages. Those groups changed their ethnic identity many times even when there was only small migration to their lands, since the particular political dominance and cultural prestige changed a lot throughout the centuries. Belgae tribes were apparently already closer, in culture and possibly even in language, to Germanic tribes, according to some a kind of mid-term between the Celts to the south and west and the Germans to the north and northeast.
Their absorbing a new cultural and linguistic layer wouldn't have been that difficult, because they were all generally part of the same cluster of more or less similar cultures, especially since it is already well accepted that there was strong Celtic influence (perhaps even via the Belgians themselves) on the early Germanic tribes, rendering them more culturally similar with the Celtic and Belgian tribes that they would eventually conquer and assimilate.