I see why Tressler and Elkhorn were robbed and why Thaddeus was framed, but I don't get why a French bank was robbed. The only hint I got from the movie was "they delivered the note" and that makes no sense to me. Was Shrike French? And have I not been paying enough attention at all?
Apparently Rhodes (Shrike's son) held the bank in Paris at least in part responsible for not paying out the insurance money after his father died.
To quote Wikipedia (emphasis mine):
And here is the dialog excerpt from the movie (transcribed myself). It takes place between Dylan Rhodes and Thadeus Bradley during the final reveal in the police cell:
I also found that explanation a bit odd, because I don't think the bank would be able to pay out the insurance money on their own either way. After all, Tressler's company was the insurance company and responsible for approving any payouts.
Maybe he just was not very rational about this and his thoughts of revenge blinded him.
Maybe he just needed an excuse to rob a bank in a stylish fashion.