Tres dix-huitieme

14:16 Sep 18, 2013 

Having lived in Seoul for 3 years IMO the "18eme (arrondissement) style" referred to in your text is NOT synonymous with Gangnam. See my answer for what it is synonymous with.

The cultural reference here is more equivalent to the red light district near Yongsan station, on the Gangbuk side of Seoul.
HTH.

13:42 Sep 18, 2013 

Gangnam is the name of an administrative section of the city Seoul, located in south of the Han river.
Gangnam style means very chic & luxurious life style.

07:58 Sep 18, 2013 

Parisians in particular often use the numbers of arrondissements in this way as a short-hand way of referring to a particular cultural aspect, etc., just as we in the UK might say 'very Sloaney' or 'a bit Soho'.

I feel sure in my own mind that if the speaker had been referring to the 18th century, they would have had to either add the word 'century', or express it in some other way, like referring to the 'Ancien régime', for example; no one style of dress could really be said to represent the entire 18th century (or any other, for that matter), unlike, for example, when in EN one might talk about 'Victorian furniture'

14:29 Sep 16, 2013 

This would help you decide whether it's 18e siècle or 18e as in Pigalle and its sex industry. IMO, from what's in the extract, either is possible