In French and English, the same symbol is also sometimes used to indicate that two adjacent vowels should be pronounced distinct from one another, instead of running them together into a single syllable. This is not commonly used any more in English, but I'm not sure about French. It is also possible that this usage has a name other than umlaut, that I'm not aware of.
In any case, an example: naïve. This word consists of two syllables, as indicated by the umlaut.