Wirelessly posted (BlackBerry: BlackBerry8530/5.0.0.1030 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)

While AA does not fly LAX-CDG nonstop, AAdvantage partner TN does. But TN award-seat availability cannot be displayed on aa.com; you must call AA.

Similarly, IB offers a seasonal LAX-MAD nonstop, with connections to both CDG and ORY; but IB award seats also cannot be displayed on aa.com.

Yet another possibility is LAX-YYZ-BRU on AA/9W. Again, you must call AA to book 9W.

But your bigger problem will be finding four SAAver seats in either Business or Economy on the same flights. So I would hold off on transferring any Starwood points to anyone's AAdvantage account yet, and consider splitting your party into two groups of two.

If you cannot find sufficient seats at the lowest award tier with AA or UA miles, I would look for LAX-LON flights on Virgin Atlantic at delta.com.

Note that AA, DL, and UA permit one-way awards. But DL one-way awards originating from Europe have hefty surcharges. So if you're going to redeem DL miles for VS, just make it one-way LAX-LON, and use AA or UA miles to come home.