Alix

Alix is also an old French form of Alice.

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For instance: http://en.wikipedia.org/wiki/Alys%2C_Countess_of_the_Vexin
"[Alys] is also known as Alaïs, Adélaïde, Adèle, Alais, or Alix." [noted -ed]

Popular in Norman times, the name was then pronounced more closely to modern "Alice" and was an early variant of that name.

As a feminine name, it is a variant of Alice (as Beatrix is to Beatrice).

Also could be from the ancient Greek word "allix", means coat.