I dont think any specific films really had anything to do with it in the long run. Im sure each filmmaker had their favorites and used that in their films but in the end I think it was simply the genre as a whole and the mythology of the old west itself.
Certain Italian(euro) filmmakers were fans of westerns and/or interested in the American west(or simply saw a chance for profit) and that inspired them to make westerns. Over time they simply devloped their own style. Just like any genre that as notable elements.