Try deleting span infront of ID, since ID is unique and can be used only once.
#me:hover {
cursor: url("links/_moi.jpg") auto;
z-index: 2;
}
Or try changing from ID to class and call it into your span.
span .me:hover {
cursor: url("links/_moi.jpg") auto;
z-index: 2;
}
<h2>My name is <span class="me">Natalie Taylor</span> and I am a graphic designer based in Frankfurt am Main, Germany.</h2>
EDIT:
While changing it to pointer without an image it works, try checking if a path to image is correct and if image file is correct (.jpg, .png, ...)
.me:hover {
cursor: url("links/_moi.jpg"), auto;
z-index: 999;
}
<h2>My name is <span class="me">Natalie Taylor</span> and I am a graphic designer based in Frankfurt am Main, Germany.</h2>