Flight time out of Orly

That's a big responsibility. Suppose someone says four hours, but your plane is late and you miss the second flight.

Personally, I wouldn't make a flight reservations on a separate ticket for the same day, even though logistically your idea of flying out of Orly is the most logical. However, no one can predict if your US flight will be on time, if you'll end up having to buy a new full-price plane or train ticket because you missed your flight, etc., or if everything will run smoothly.

Here's what I see: to be absolutely safe, you need to reserve for late in the day. So first choice is hanging around a pretty disagreeable airport all day. I'd take choice two if it were my itinerary: check into an Orly hotel, go into Paris until evening, come back to the Orly hotel, sleep and catch a very early flight to BCN the next morning. Definitely not the most efficient, but safe.

Its a gamble but I've done it many times and have never had a problem
The worse that will happen of course is what the previous poster said; you may have to buy a new flight.
When you search you will see Ory to BCN you will see a lot of non stops
Since you are scheduled to arrive at 10:05 am Go for the 15:15 or 16:45

It makes no difference what alliance what airline you fly.
They all arrive late sometime or another
but someone here who may have been traumatized will irrationally say oh sh** British Airways avoid this that...

I don't like to do it but I have. I recognize that it is a risk but recognizing risk and managing it are two different things. I manage the risk a couple of ways. If the subsequent flight is expensive or if there are not a lot of flights, I leave 8 to 9 hours -- for real. If the subsequent flight is not going to be a budget buster if I buy the ticket on the day of the flight and if there are frequent flights, I leave a four hour gap. And I only do this when traveling alone or with the one other person I know who will not be unpleasant if the connection fails -- my husband.

Is a multi-destination ticket out of the question? For instance: US to Barcelona (probably with a transfer somewhere) and then home from France. Often these joint tickets are not much more expensive than a city-to-city round trip, especially adding in what is saved in returning to the original landing airport and and time lost. They're easier and the connections are guaranteed. Stress is expensive. Buying a single ticket to Spain from Orly on a budget airline will probably force you to go through immigration security (the real delay) as well as retrieving your bags and checking back in for the next flight.
If you fly BA, you might find yourself changing in London for Barcelona, with the second leg of the itinerary guaranteed in case of delay. Returning from Paris you might be on a one-stop BA flight or one of its partners direct.
My favorite information site is www.maxtrix.itasoftware.com, run by Google for the airlines so it doesn't sell tickets, but it does cover a lot of options. (For budget flights in Europe, www.skyscanner.com)