The calculated distance (air line) between Le Puy-en-Velay and Nîmes is approximately 87 miles respectively 139 kilometers.
By car or train, the actual journey to Nîmes is certainly longer, as only the direct route (as the crow flies) between Le Puy-en-Velay and Nîmes has been calculated here.
Air line (approximately)
139 kilometers
75 nautical miles