Help - International shipping question

Can anyone advise me if there is a way - any way - to ship a box that weighs approx. 7lbs to France without spending an arm and a leg? The items I am shipping are too big to fit into the long, rectangular new Priority Flat Rate boxes - so the box would be slightly larger than that. Even if they did fit into a flat rate box, if I am reading the USPS site correctly, it costs $37.00 to use it (and there is a 4 pound max anyway for international anyway). I specifically say in my auctions that I ship to USA and Canada only, but a bidder from France bid and won anyway - and whenever that happens, I try to accomodate them. But, this time I don't think I can - thanks for any help!

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Now that the PO no longer has surface mail it's going to cost at least an arm to ship any kind of poundage to Europe. You might check FedEx, DHL and UPS for their rates but I don't think it will be any better.
I learned the hard way when rates changed...listed some stuff I normally do (computer parts) and won by folks in Europe. I used old listing templates and forgot to edit the shipping. I had no choice but to eat the cost.