He can touch you, but he isn’t supposed to be intimate with women that are not his family or that he is not married to. It is a minority within muslims that carry that notion of not being intimate so far as that they cannot touch women at all.
We live in a very (the most?) Islamic country and we very, very, very rarely come across a muslim that refuses to shake my wife’s hand.
(The reasoning is that all that leads to haram is haram and touching a woman’s hand may trigger haram thoughts.)
However… there are many different interpretations and I am sure their views differ.
Anyways, even then: any muslim, if he really wanted to, could marry you and then all would be fine anyway.