Is the trait of being female caused by a recessive gene?

No, xx is not a recessive gene pattern, they are chromosomes. In a sense, one can think of female as the "default setting," if you will, because as long as you don't have any Y chromosomes you will be female. The addition of a y chromosome will give you male characteristics (although I'm broaching into genetic deformities,) but that does not mean that being female is recessive.