The shortest English word containing all five vowels is EUNOIA (the goodwill a speaker cultivates between himself and his audience according to Wikipedia). More common such words, but with one more letter, are SEQUOIA and EULOGIA.
The shortest such French word is much more common. OISEAU means bird.
The shortest English word with the five vowels in alphabetical order is AERIOUS (meaning airy). I personally like FACETIOUS, which is a bit longer. Note that FACETIOUSLY has all six vowels (Y is both a vowel and a consonant in English).