TL,DR: take RER B to Denfert-Rochereau. Buy an Orlybus ticket. Take the bus when it's time to leave for Orly (allow 30min travel time + ~20min interval between buses + risk of delay).
The Paris airport authority website has all the travel information. Refer to it for stop information.
The quickest way to transfer between the two airports off-peak is a taxi, but it's also expensive — at least €50, more at night or on Sundays. A taxi should make the trip in about 30–40min if there's no traffic, but at peak hours, the taxi can get stuck in traffic jams for hours, so I wouldn't recommend it.
Cars Air France
The most comfortable option is the bus. Air France runs a bus between CDG (terminals 1 and 2 — from T3, take the shuttle to T1) and Orly (West and South). The advertised journey time is about 90min (but it should take a lot less off-peak), and there is a bus roughly every 30min. As this is an airport bus, there'll be plenty of space for luggage, and you'll get comfortable seats.
You can take the train: RER line B between Roissy CDG and Antony, and Orlyval between Antony and Orly. You buy a combined ticket for RER+Orlyval; note that the RER part depends on the station you get off, so make sure to get an Orly–Roissy ticket and not an Orly–Paris ticket. Off-peak, all RER B trains from Roissy CDG go via Antony; at peak times and in the evenings, you may need to change in Paris. Going the other way, from Antony, make sure to board a train going to Roissy; depending on the time, you may need to take a train to Paris and change (change in Paris Nord as a few trains depart from there). The journey should last about 90min, but allow for delays, especially during peak times.
As an alternative to Orlyval, you can change at Denfert-Rochereau for a bus, see below.
Coming from Roissy, you'll get a seat on the train. Be sure to keep your luggage out of the way as the train can get very crowded while crossing Paris, and watch out for grab-and-runners. In the other direction, the train can be standees-only in Antony already. You won't have to climb any stairs whether going via Denfert-Rochereau or Antony, unless the elevators are out of order, which happens more often than it should.
A break in Paris
If your flight is on time, you do have the time for a quick coffee and baguette, but watch the time. My recommendation would be to take RER B and get off at Denfert-Rochereau. From CDG, get a ticket to Paris (it's the same ticket wherever you get off within the city limits; on line B, the stations from Gare du Nord to Cité Universitaire are within the city limits). There is no shortage of cafés and boulangeries, and there is a small park right outside the station. From Denfert-Rochereau, take Orlybus to Orly airport. Note that changing at Denfert for Orlybus is an option even if you don't want to stop: it's slightly cheaper and about as much hassle as changing at Antony Orlyval. The Orlybus route is very slightly riskier at peak times but the bus has a dedicated lane most of the way (and RER B isn't a paragon of reliability anyway). The travel time is normally 20–30min and there are buses roughly every 20min. If you get off the RER at Denfert, you can't use the same ticket to continue south: you'll need a separate ticket for Orlybus (which you can buy at Denfert) or a Paris–Orly ticket if you decide to continue via Antony.
If you have a little more time, you can get off the RER at Cité Universitaire and eat your baguette in Parc Montsouris, but there are fewer options to buy the baguette and catching Orlybus is harder (you need to find the Stade Charléty bus stop, one tram stop east from Cité Universitaire). Other possible stops are Saint-Michel-Notre-Dame (close to the famous Notre Dame church), Luxembourg (near the eponymous garden) and Port-Royal (a relatively quiet place but no park). Gare du Nord is an option if you want to walk around some seedier neighborhoods north of the station, and Châtelet-les-Halles is an option if you like underground shopping malls. (Yeah, I thought not.) All of these require a further ticket to continue towards Denfert to take Orlybus, and given the extra connection required after the baguette, I don't recommend them in your case.