The best option is to pay for the night before in the hotel and arrive early to a room that is ready.
Second option is to take a day hotel at the airport, go in, take a shower, rest a little and then go to Paris.
Next option is arrive at the hotel and ask very nicely. Look tired, smile a lot, look excited at being at the hotel and ask if they have a clean room ready for you.
If all this fails, leave suitcases in the hotel, let them know you would love to have a room, ask them when you should return and then go out.
I would start by having a nice breakfast - not too heavy with lots of good strong coffee. Spend an hour or more enjoying the morning rush hour of people buzzing around.
Take a long stroll, maybe go to Luxembourg gardens or the Tulleries and spend an hour enjoyed the view. Walk up and down Champs Elysee which is always busy with lots of people and coffee shops if you need a little extra boost of energy
At one o'clock I would go in for a long lunch and walk back to the hotel. If room not ready sit in the lobby and take a nap.

You should also consider asking your doctor for some sleeping/chill pill so you can at least sleep for a few hours on the plane.