There are too major factors as to why the Tour is bigger, and they were set in the early 1900s.
Location-Cars were barely in existence, so you had to go nearby to ride in races. France is bordered by Belgium, Spain, Italy, Germany, Luxembourg, Switzerland, a few of these being true cycling mad countries, while Italy is mostly bordered by water. IT was easier to get to races in France.
Established Races- When the Tour had started up in 1903, you already had a few established races, including Paris-Roubaix (1896), Paris Tours (1896), Bourdeaux-Paris (1891), Paris-Brussels (1893), L-B-L in Belgium (1892), were already established and had started to become yearly ran in 1900s.
Italy oldest races are Giro Di Lombardia (1905), Milan San Remo (1907), Milan-Torino (1876, but only had 6 editions before it went back to back years in 1913) Giro del Piemonte (1913), Giro Del Veneto (1909), Giro Dell Emilia (1909), Giro della Romagna (1910),
I am sure there are other races im forgetting, but these are the ones came off the top of my head. International cyclist had already established something in The Paris area for a few years before the Italian races were created.