OneWorld NYC-PAR USD 1951
 

Business class direct flights with Openskies, AA or Aer Lingus (not direct), Mondays and Tuesdays in Nov and Dec and maybe other months. Other days may cost a bit more.

May be even cheaper with AARP and Visa rebates for BA/Openskies.

Skyteam is close at 2,300.

Nice fare! In response La Compagnie is lowering their fare to $1500.
AARP should apply to the BA flights this year - not next year however as the AARP deal ends.
Note that a minimum 7 day stay is required. Sample fare: https://goo.gl/flights/6GJR

This works over Thanksgiving and Christmas as well.

There's also BOS-BUD on BA for USD$2145, looks like through EOS.