No, it doesn't matter (at least not to Google and Bing). My language has a number of accented characters and searches both with and without the accent return the same results.
Most tellingly, the highlighted keywords in the search results snippets ignore the accent.
Google also seems to handle some common substitutions. For example searches using a 'd' where an eth 'ð' should properly be used, will turn up results with the correct spelling. Bing fails on this one.
All in all, you are perfectly safe in using "Zoë" on your site, at least as far as Google and Bing is concerned. It will also have the bonus that any searches where the 'ë' character is used, you will turn up higher as you aren't competing with the plain "Zoe" search term.