I hate to make the comment that your wife might really enjoy Business Class a lot more than coach.

That said . your options are even more limited. Possible I-fare sale still in effect at $2591/per/+tax. And it would earn miles as a J ticket.

As mentioned .. LHR and then cheap flight or Euro-Star.

Guess surprising someone with a coach ticket for a romantic get-away is not my idea of a 'hot' surprise. Business would be the MINIMUM I would want to be surprised with!