The issue of distinguishing between Celtic or Germanic roots of modern placenames (toponyms) is currently being discussed on the continental-celtic mailing list. The dates of various sound shifts, and basically who spoke what when, is under vigorous discussion.

As part of that discussion, Richard Baudette put together this interesting page with a map of which regions, in his view, spoke which languages during the second century bce. Notably, he has a broad swathe of a language he labels as 'Belgic' (corresponding to Caesar's mention of Belgic, Celtic and Aquitanian as the three languages of Gaul, and thus taking the Seine as the south-west border) and suggests that, although Indo-European, it was neither in the Celtic nor the Germanic family.

This is then used to explain, for example, the observation by Pyt Kramer that:

In his still valuable work Hans Kuhn (1966) reports 6 mans names of Frisians in the first century, from which only one is explainable from Germanic. He concludes that the new [Germanic] language had not succeeded entirely yet at that time.

In the Netherlands and the Nortwest of Germany there is an important old layer of placenames that are not Germanic, but many of which show IE p- and therefore are also not Celtic. Even the tribe name of the FRISII itself is net well explainable from Germanic.

However, Chris Gwinn disputes any degree of mutual intelligibility or closeness between Gaulish and Germanic, or that Belgian might not be Celtic, saying:

You seem to suggest that Celtic and Germanic were particularly close linguistic relatives, but aside from obvious loans from one language to the other, I don't think there is much evidence for this - Celtic is much closer to Italic than it is to Germanic, anyway. Furthermore, there is no good evidence (IMHO) for Belgic being drastically different from Gaulish - all the onomastic material points to virtually the same language being spoken by both the Galli and the Belgae. We know that Belgic must have been spoken in areas of Britain, but I think you would be hard pressed to distinguish Belgic from earlier strains of Brittonic. I don't see any evidence for Belgic being any closer to Germanic than any of the other Celtic languages.

I hope this report 'from the trenches' helps show both the complexities and also that there is active disagreement among scholars in this area.