I don't know what you mean by rigid word order. If you mean syntax, I am sure that a large percentage of other languages have much more rigid ones. In English there are things you can say in a variety of ways (it's how we have passive and active voices, etc.), while other languages are so strict (like you say, due to gender rules and other rules) that it is difficult to be ambiguous in any way.
I consider Spanish to be probably a polar opposite, as it consists of several rules, truly rigid grammar, and that there's actually a group of people dedicated to deciding what is proper and what isn't (La Academia Real de la Lengua, I believe.) If I'm not mistaken this is the case with most romantic languages.