A valiant attempt to achieve this with a commercial flight will look something like this. You'll need a mobile phone with data, passport and credit cards or cash (EUR and USD) on you at 13:00, just to make the attempt.
At 13:00 you go immediately to the Air France web site, and book a ticket on AF006, which is scheduled to depart CDG at 14:05. Then you check in online for it. You must complete these before 13:05, because check in closes an hour before departure. (You probably won't be able to do this in five minutes unless you already have a login with Air France and have booked flights with them before, so that they have your details already.)
You then find a taxi and pay the driver to get you to CDG Terminal 2 as fast as he can possibly go. If he drives normally, you ought to arrive around 13:30, but hopefully you will gain several minutes from a very aggressive taxi driver.
Along the way, you empty your pockets of anything metal you might be carrying and don't need, so that you can speed through airport security later.
Boarding closes 20 minutes before scheduled departure, so you need to move through the airport and get to Terminal 2E fast. Walk through security and passport control, and then check the departures board to find your gate.
You picked the right taxi driver today. As you are looking at the departures board you hear the final boarding call. You run to the gate and are the next-to-last person to board.
Unfortunately there's some kind of problem, and the plane doesn't push back right away. 14:05 comes and goes and it's still sitting on the ground. There's an announcement of a "short delay" but no actual explanation. You look out the window and the weather seems fine. It's only been mostly cloudy with a moderate breeze all day and it's only mostly cloudy now. Even though you know you can do it again if necessary, you're just as impatient to take off as everyone else is.
Finally, some 40 minutes late, the plane pushes back, taxis to the runway and takes off. A few people start applauding and then quickly stop. Nobody ever explains exactly what delayed the flight.
You think about what lies at the end of the flight. It's scheduled to arrive at 4:20 pm, which only leaves you 40 minutes to get through immigration and find a way to Times Square. But with the plane having left 40 minutes late, you're pretty certain you won't make it at the end.
You're in luck though. The plane caught some good weather over the Atlantic and made up all the time it lost. You arrive at the gate at exactly 4:20 pm, the scheduled time. Since you don't have any luggage, not even a carry-on, you get up and squeeze past as many people as you can, heading toward the exit.
Even so, you don't get ahead of everyone, and by the time you get to the end of the jetway, you can see that Terminal 1 is a complete zoo. There must be 500 people here! Your passport lets you use the automated passport control kiosks, but there are still what seems like dozens of people in front of you. You finally get to a kiosk, fumble your passport into the reader, and punch a bunch of "No" declarations into the screen. Finally you run past the baggage claim and make it to customs, where there's another seemingly endless queue.
While waiting your turn to speak to a customs officer, you suddenly find yourself back under the Eiffel Tower. To get to Times Square, you needed another 37 minutes that you just didn't have.
On this do-over, you don't even bother to leave Paris. You spend the day on the Champ de Mars and begin to think about where you can shave off minutes or even seconds on your next attempt. Maybe there's some way to figure out what delayed the plane, and get it to leave on time on a future do-over. Perhaps there's a way to get through immigration faster? Probably not, with those huge crowds. Can you sneak past them somehow? And if you do, will they spot you? What happens if you get to Times Square on time, but with 50 cops in pursuit?
Obviously this is going to take a while to figure out. Fortunately, you seem to have plenty of time to do it with...
Note: This post incorporated Air France policies, actual historical flight data for AF006 and actual weather conditions in Paris for 2 July 2016. Also consulted was CBP immigration wait time data for JFK Terminal 1 (which unfortunately can't be hyperlinked).