Hyp said:
I don't even know how that's supposed to be pronounced.
Well, in French at least, the ^ sign is used on letters that were previously followed by a "s". For example, hôpital, hôtel, île, forêt. (I choose those example because their old form is still kept in English.) The pronounciation of â, ê, and ô are modified from those of a, e, o, but not those of î and û.
The ¨sign is used in French only on i and e. The ï is used to avoid diphtongs, because "ai", "ei", and "oi" are special sounds. aï, eï and oï are thus akin to "ahi", "ehi", "ohi".
In German, the ¨is used to change the sound of the vowels a, o and u.