At 3645 m, the (reportedly) highest European mountain accessible by regular hiking (no glacier gear) is Monte Vioz (https://en.wikipedia.org/wiki/Monte_Vioz) in Trentino, Italy. The climbing season streches from June to September.
Another similar mountain, though not the highest one available, is Hochfeiler / Gran Pilastro, 3510 m, in South Tyrol, Italy, on the border with Austria, but accessible only from the Italian side. Unlike Monte Vioz, I've already climbed Hochfeiler and it was a spectacular adventure, highly recommended.