American Airlines requires 57,500 miles for one-way travel between the continental U.S. and Europe. You can get to Frankfurt for that amount on Sept. 11 or 19th. You can return for that amount on Sept. 20, 21, 26 or 27. (Other dates may also be available for that number of miles, or some of those may no longer be available, by the time you check. If a date isn't available for 57,500 miles, it is probably still available for more miles, but you don't want to do that unless you have no alternative.) That's a total of 115,000 AA miles for the round trip. Getting those will require 95,000 SPG points because of the bonus that Duke787 mentioned above. You can even take a friend!
The routing I got for that itinerary on the random pair of dates I used has you on an AA commuter hop to San Diego, then BA with a change in London. Depending on where you are in the LA area it might be easier to just fly out of SAN. You won't save any miles by doing that, but you'll avoid the need to deal with LAX.
You can book this online with AA, but I'm fairly sure you have to move the points into your AA account first to do it. You may be able to put it on hold while you move them. The AA and/or SPG forums here will probably have more information about that, or you can call AA to find out without incurring a telephone booking charge as long as you don't actually book anything with the phone agent.