I would like to change the font on the footer, but not the header.
I don't think this can be done, the header and footer share the same
font selection option.
However, are you sure you want to use headers and footers? Using a
background page can provide better results. Add a new page and make it
a background page. Add this background to the normal pages. Now on the
background page add text boxes for where you want your header and
footer data. For each box do a Insert -> Field and add the appropriate
data.