> The image of ***a*** European dressed in **his** finery going out to gaze upon...

In this particular case, you're talking about *just one European*: "dressed" is referred to *one* of them - no matter what his/her sex is: it's just *one person* and you should use a singular possessive adjective. You should have used *their* if the noun to which "dressed" is referred had been "European people" or something similar.