The problem I am having is that when I call sort() on my array of strings, it alphabetizes it fine, except for french strings.
It will sort it like so:
Atlantic Inc.
Bait Inc.
Zack's Fish Mart
Émile Fisheries Inc.
What can I do to sort both languages appropriately?
The sorting rules are highly dependent on the locale.
You can force a locale using the SORT_LOCALE_STRING flag:
http://php.net/manual/en/function.sort.php