October is the sweet spot for this route. Days settle into a gentle 17-22C across Rome, Florence, Cordoba and Bordeaux, exactly the range where a dog can walk for hours without panting, and the summer crowds have gone home. Vienna and Brno turn gold, parks and vineyards alike, while the Mediterranean beach bans lift on 1 October, so your dog is welcome back on the sand in Cordoba and along the coast near Rome.
It is also harvest month. Bordeaux and Moravia (Brno's wine country) hit their grape-picking finale, with cellar doors busier but friendlier, and pet-friendly courtyards perfect for a slow lunch. Cities feel emptied out and lived-in again, hotel rates drop from peak summer, and the light turns that low, golden hour that makes every piazza and riverbank photograph well with a dog in frame.