I always thought it came from lapis lazuli (portuguese). Azul as a subpar of Lazuli even sounds exactly the same in portuguese.

Lapis Lazuli is cognate, both come from the same Arabic/Persian root. Apparently “azure”, “azul”, “azzurro” lost the L because it got confused with the common “l’” article,

And the word from arabic comes, for both of them comes from persian for hte term lapis lazuli (lāžward) and suposedly this comes from sanskrit... but I ignore how it may sound in sanskrit.

In french we have “azur”