German logistics and a southern French redoubt

Could Germany simply keep advancing through southern France if resistance continued?

Not easily; German logistics were near exhaustion, creating a race between German resupply and French reorganization.

The possibility of continued resistance depends on the weaknesses of both armies. France was disorganized and losing industrial capacity, but German formations had advanced beyond their logistical plan. Fast armored spearheads still depended on a supply system heavily reliant on horses and increasingly unreliable vehicles. Without fuel, food, ammunition, and maintenance support, battlefield superiority could not automatically carry the German Army through the rest of France.