The ancestry of Bertrada is unproven. The suggestion that she was daughter of Theoderic III is based on the inheritance of Rommersheim jointly by Charlemagne's parents. Another theory relates her to the Merovingians only through marriage.

Peter Stewart

We can identify a group of sisters (or at least close female kinswomen) that includes Bertrada, but there are several different theories as to the identity of their father. I think it was Maurice Chaume who speculated they were daughters of King Theoderic III, but more recent scholarlship tends to favor Count Hugobert.

Todd A. Farmerie

... the predominating opinion these days is that Bertrada (not Bertha) mother of Charibert, was daughter of a Count Hugobert. He was perhaps of Merovingian descent, but no ancestry is currently known for him.

Todd Farmerie (Mar 6, 1999)

The ancestry of Berta, merovingian or not, can be the subject of a lenghty book. But in a few words, I can give the reason which make probable, for Chaume (who nerver make of Plectrude a merovingian princess), and others, including myself, her merovingian affiliation :
We know that the villa of Rommersheim is the common property, inherited of their respective fathers, of King Pippin and his wife Berta, daughter of count Charibert.
So, given merovingian successoral practice, one person have two children, one being Pippin’s father ancestor and the other Berta’s father ancestor. Otherwise, we know that Rommersheim was previously in the hands of Berta « of Prum » and that she had in 721 one only surviving son named Charibert.
So the first conclusion is that Berta’s son Charibert is the same that Charibert, father of queen Berta. The second is that Berta of Prum was akin of Charles Martel. E. Hlawitschka has build an elaborate theory which make of Berta the sister of Plectrude, the second wife of Pippin, Charles’s father. He denied so merovingian ancestry for Berta. So the standard theory. But this theory is a misconception. He does so only because he fails to find a « natural » link between Berta of Prum and Charles Martel on the ground of ecclesiastical prohibitions. But this failure is due to his inadequate search.
Merovingian blood for Berta is expected for onomastic reasons (her name , her son’s name , her grandson name are all merovingian names). And this explain the merovingian names given by Charlemagne to is children (not only first sons, Clovis and Clotaire, but another son, Theoderic, and a daughter, Clotilde).
A good explanation is that one :
The king Theoderic III has a wife Doda. This Doda could be a daughter of Ansegisel, son of another Doda. So, Ansegisel, presumably share Rommersheim between his son, Pippin of Herstal and his daughter Doda, king Theoderic’s wife. Then Pippin’s son, Charles Martel inherited that, and so Berta, Doda’s daughter. This explain why King Clothar IV, son of Theoderic III, was called the cousin of Charles Martel in Ademar of Chabannes’ chronicle.

Settipani (Nov 16, 1999)