Go to Tour Eiffel

It would be very risky to go into Paris, see the Eiffel Tower and then get to Orly in good time. Remember that you have to go through Security at Orly and that could be lengthy. If you google "transfers from CDG to Orly" you will find the various ways, and yes, you do have to organize this yourself.

The simplest way to get from CDG to Orly is the Air France bus. It won't take you into the city at all but it will get you from one airport to the other with no trouble. You have to do it yourself, but that just means being where the bus leaves when it leaves. If you miss one, or it's full, you'll have time to get the next one.

It might be possible to travel into Paris, with luggage, get to the Eiffel Tower, maybe get to the top (with luggage), descend, then go on to Orly, check into your flight, go through security, and reach the gate in time for boarding. But I would not know how to do it and I would not take the chance. To avoid long lines you will need to buy an Eiffel Tower ticket in advance, for a specific time. If your flight arrives late, or you have to wait at immigration and customs, or you have trouble getting into Paris, you could easily miss your time. Then you could look up at the tower from below (quite an impressive sight) and resume your journey to Orly.

Have a good trip but don't try to see Paris is such a short time. That said, you may get brilliant ideas from other posters with more Paris experience than I have. : )

The Eiffel Tower is just as magnificent seeing it from the base and looking up. You don't have to go to the the top to enjoy it.

See also these transportation notes for connecting Paris airports.