Under siège

Two days ago, Languagehat posted a couple of interesting points about translations of French in the New Yorker. For our purposes, the relevant part is:

First is the odd quote on p. 64, claiming that Chirac called the veil "the siege of a politics of Islamization." The first noun clearly represents the French word siège, which in most contexts (and certainly this one) means 'seat, locus'.

At first, I just absorbed this as an interesting factoid. It wasn't until just a few minutes ago that the light bulb went on about the first place I ever heard of a siège.