According to a NYT article [1] from the 2003, when the Concorde flew it's last flight, the airlines have never disclosed exact numbers for the profitability of the Concorde. Air France said 'Concorde operation was profitable "in some years."' BA said it once was, but not after the AF Concorde crash in 2000.

They specifically mention that both Airlines didn't have to pay for the planes:

> Part of the reason the airlines could claim some profitability on the Concorde was because they did not have to incur capital costs on the planes. [...] The governments of England and France underwrote the costs of building the 14 Concordes, which were then turned over to the two national airlines.

[1] http://www.nytimes.com/2003/10/24/nyregion/for-concorde-econ...

My grandfather was one of the first pilots in Air France. He refused to fly the Concorde because he would never fly a plane that would make the company loose money.