Common words:
* Un (a, an)
* Une (a, an - feminine)
* Unité (unity)
* Univers (universe)
* Utiliser (to use)
* Urgent (urgent)
* Usine (factory)
* Utile (useful)
* Uniforme (uniform)
* Utopie (utopia)
Less common words:
* Ubac (northern slope of a mountain)
* Ultime (ultimate)
* Ustensile (utensil)
* Ubiquiste (ubiquitous)
* Utopien (utopian)
Proper nouns:
* Ukraine
* Uruguay
* Ursula
This list is not exhaustive, but it gives you a good starting point for French words beginning with "U."