The German miltary used just about every piece of military or transport equipment they could get their hands on. French and Italian vehicles were acquired wholesale after the occupation of the two countries. Enough vehicles were acquired (along with sources of spare parts0 that a regular supply chain existed. Most of the equipment would have been used by the garrison occupying the country, although one source I saw showed the Afrika Korps had several battalions of coastal artillery equiopped with French heavy artillery.
Transport vehicles were both easier to maintain and less(?) likely to be exposed to front line combat. In addition, Ford and I believe Fiat had licensing deals European countries between the wars; so parts should have been available.
If all else fails, comandeer anything that rolls from the local civilian population.
Groundlber
Captured Vehicles
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