Paris is the capital city whose metro system is famous for running trains on rubber tires.
The Paris Métro pioneered rubber-tyred metro technology after the Second World War. The system combines rubber tires running on special rolling surfaces with conventional steel wheels and rails, which provide guidance and an important safety backup. The arrangement gives trains strong grip for acceleration, braking, and steep sections.
Rubber-tyred operation entered the Paris network in the 1950s. Today, Lines 1, 4, 6, 11, and 14 use the technology, while other Paris Métro lines remain steel-wheeled. That distinction is the key detail commonly missed: not every Paris train runs on tires.
The Paris design influenced metro systems abroad, including those in Montreal, Mexico City, Santiago, and Lausanne. Montreal is sometimes offered as the answer because its metro is strongly associated with rubber tires, but Montreal is not a national capital; among the listed capital cities, Paris is the canonical answer.