What exactly do you mean by Frankish identity? Do you mean French identity? Because if you look you'll find French actually is not descended from Old Frankish, but from Latin. You'd be better off asking what happened to Germanic identity in France (and I couldn't really answer you there).

If you're talking about (West-)Germanic identity, it's still there. Dutch and German are very similar languages, and there's a lot of cultural and historical similarities (don't say that to a Dutch person though).

If you're asking about why the Low Countries specifically became their own cultural unit. Well, lots of reasons, but a large part of it is simple politics. The Low Countries ended up being unified in the Burgundian Netherlands in the 15th century. Over the course of history this territory became politically independent from its Germanic neighbours to the east, and developed its own national identity. With each of the three Benelux nations having their own idiosyncratic histories.