Some reservations can only get by post to you at home (TGV/AVE Barcelona to France. Some reservations can Eurail.com only do on paper, but other train companies can do it online. 

Please say to us, where you want to go, so we can advise to book reservations via an other retailer. 

I am traveling from Paris to Barcelona, after Barcelona Avignon 

This train between France and Barcelona (Spain) needs the reservation on ticket paper and mailed by post. 

Will reservations be mailed to my home in the United States 

How long does it take for reservations to be received by me in the United States?

Im sorry, I have no idea, but they should tell you before booking. Maybe some one else will respond to this thread.

Paris to Barcelona and Barcelona - Avignon will be sent via e-mail if you book via SNCF by phone (press #85 for English). No booking fees or postage fees, but the phone call is not free of course.

In that case you get a code/nr which you have to use to retrieve ticket fro a SNCF machine-just follow instructions. Or maybe even a direct mail with the QR-code needed to board.

And yet again-as it seems any newbee wants to use exactly these trains that are the hardest to get: with a little longer time and more changes its perfectly possible to to BCN-AVI just by local trains-more views, more chance on a short stop en-route. But you save at least some 30€ doing that-or only use TGV IN FRance for 10€ and not overtheborder.