Most people only relate the "odd" Paris/London to/from New York routes to Concorde, but she did far more than that and also on a regular basis. They've just reduced her to these main routes later on, while the charter branch took all kinds of destinations into account, including the world tours.

But Braniff was indeed an operator of Concorde, I think in both (AF/BA) colours but with a complete Braniff crew. For over a year they were running that service.
They even mentioned it here. http://en.wikipedia.org/wiki/Braniff_International_Airways
That's a special thing since the routes did not include any supersonic stage at at all.