First things first is to have a look at what Ford-Werke (Ford's existing German subsidiary) had on offer around this time, which were basically LHD versions of what existed in the British market. Even when given German names, like
Köln or
Eifel, they were just basically localized versions of what already existed outside of the US - in this case, the
Model Y and
Model C (both smaller than North American Fords, and indeed the latter replaced the former in 1937).
Now, had Ford decided to take on the KdF-Wagen (aka VW and the associated facilities), my thinking is that it would be directly integrated into Ford-Werke and not given any special treatment. It would definitely upend any possible plans for the Taunus, meaning this photo:
gets butterflied away. Ford would just simply relocate everything from Cologne to Wolfsburg, at least temporarily, reducing its former facility to making components and parts before upgrading to larger vehicles as the German economy recovers.
(Image source: <
https://commons.wikimedia.org/wiki/File:Bundesarchiv_Bild_183-2005-0722-512,_Köln,_Erster_Ford_Taunus_läuft_vom_Fließband..jpg>)
New products need new names, so Ford could just simply recycle the Eifel name. Rather than seeing it as just transplanting its OTL success to TTL, I would instead scale it down to something more modest and limited primarily to Germany and maybe a few other Western and Central European countries that also IOTL took in the Taunus. (The remainder would take in its OTL British equivalent,
the Anglia/Popular.) As Ford rebuilds, the new Eifel would be seen as a little brother to
the Taunus (and probably last just as long as the 1955-1962 version of the OTL smaller model). Consequently, the Eifel proper would be limited to just simply the 1950s, with that particular model not continuing beyond the early 1960s at the latest.
However, if the consolidation of Ford's European subsidiaries becomes a thing and the Anglia and Eifel lines eventually merge, it could theoretically have influence on Ford's C-segment models over the long term (regardless of whether or not it's similar to the OTL Escort) but in a more modern and attractive package. The Eifel (< KdF-Wagen) was already outdated by the 1950s, yet few Germans cared since they were happy to have any set of wheels on the road. What
could happen in response to the Eifel, though, is that Opel develops the Kadett a decade earlier than OTL (so that Opel would retain its dominant position in the German market), and as the Kadett would be a more modern 1950s design to the outdated 1930s design of the Kadett, German buyers eventually flock over to the Kadett instead. Yet both the Eifel and the Kadett would show a market definitely exists for the C-segment, so Ford would want a newer model to take on the Kadett than the Eifel. Another legacy of the KdF-Wagen project for Ford, of course, would be the Wolfsburg factory, which could become a great asset for Ford Europe in the long run.
But, as far as I can see it, that would be the extent of the *VW Beetle as a Ford. No convertibles, no Karmann-Ghias, no Passats or Sciroccos, nothing like that. The Beetle would just simply be a curio for a certain period in German auto history before becoming replaced by more conventional Ford products, that's all. (Likewise, I doubt Ford would be that keen to expand Lincoln and Mercury vehicles beyond North America post-war.) It could bounce around in the Global South for a while longer (the
Ford Corcel and its offshoots are what I'd think of here as possible analogs), but that would be for a specific purpose and nothing like how VW grew and developed IOTL. There's probably far better alternatives for HFII's "Euro car" than the Beetle.