What is the difference between a marque and a brand?

Semantically in OP's context the two words have the same basic meaning. They both identify either the actual manufacturer or a specific product range from that manufacturer.

However, there is a subtle difference perceived by at least some advertisers, and implied by dictionary.com's definition which gives luxury or racing car as likely things to which marque may be applied...

The word marque (perhaps because of its 'exotic' French origin and associations) is generally understood to be a slightly more 'upmarket' term. Asda/Walmart sell their 'own brand' products, but I think many of us would feel it was pretentious in the extreme if these were to be promoted as being under their marque.

Marque is primarily associated with 'quality' automobiles, but it also commonly occurs with other luxury brands such as Dunhill smoker's paraphernalia, and Christian Dior in the world of haute couture.

A marque is synonymous to a brand or model. See this excerpt from the Wikipedia entry for brand:

In the automotive industry, brands were originally called marques, and marque is still often used as a synonym for brand in reference to motor vehicles.

And thefreedictionary.com claims that they are synonymous:

Marque: n: A model or brand of a manufactured product, especially an automobile.

However, marque is less common, as this Ngram illustrates:

http://ngrams.googlelabs.com/chart?content=car+marque%2Ccar+brand&year_start=1800&year_end=2000&corpus=0&smoothing=3

This is due, at least in part, to the more refined usage of marque, for upper-class or luxury products. This usage most likely evolved because marque looks and sounds more refined than brand or model, and hence came to be used of more sophisticated products.