In my magazine (and all other mainland official media) we're only allowed to refer to it as the former French Concession. In English conversation, people say "French Concession" all the time. And we all understand it to mean "the leafy- tree-lined area of town with all the best boutiques and cools bars" NOT "the area of town under French rule." However, Chinese people never say "French Concession" when they speak in Mandarin, they call it by its district name, Luwan or Xuhui.
Shanghaiist has translations of outraged Netizen reactions. I don't think they're indicative of the average Shanghai resident's feelings. Nationalistic fervor has a way of boiling over on the microblogosphere.
The analysis around the water cooler seems to be Pizza Marzano is being made an example. Shanghai Daily reminds that: "In 2001, a real estate company was fined 64,500 yuan (US$10,237) for stating in a leaflet that an estate 'retains the romantic atmosphere of the French Concession days.'" Yikes.