This is a long shot but I figured if anyone can come up with a creative solution it would be this forum.

My wife and I will be going on the following trip later this year. I'd like to use a lounge in CDG to shower (I've read some lounges are equipped with showers) and to rest for the ~5 hour layover on the first leg from ORD to DXB. I'd also like to potentially use the lounge on the way back to Chicago at CDG (notice I'll be flying from DXB to CDG and staying there for a couple days), but that isn't as important as the first leg. What are my options? I don't have any status with Delta. I have about 12K+ miles accrued over the years. I am willing to apply for a Delta SkyMiles credit card if that helps with access but I can't seem to find any that outline lounge access specfically.
I don't think a one day pass will work because according to this chart, one day pass holders are not allowed in CDG lounges.
Link
Sun, Nov 20, 2011 Chicago O'Hare International Airport (ORD) to Dubai (DXB)
Depart: 05:10pm
Arrive: 08:35am
Chicago, IL (ORD) to
Paris, France (CDG)
Air France
Flight 3603 operated by Delta Air Lines
Economy Class
(on Boeing 767)
1 Stop – change planes in Paris, France (CDG)
Connection Time: 4 hrs 55 mins
Depart: 01:30pm
Arrive: 11:00pm
Next day
Paris, France (CDG) to
Dubai, United Arab Emirates (DXB)
Air France
Flight 3830 Economy Class
(on Boeing 777-300)
Tue, Nov 29, 2011 Dubai (DXB) to Paris Charles de Gaulle Airport (CDG)
Depart: 01:30am
Red-eye
Arrive: 05:55am
Dubai, United Arab Emirates (DXB) to
Paris, France (CDG)
Air France
Flight 3831 Economy Class
(on Boeing 777-300)
Fri, Dec 2, 2011 Paris Charles de Gaulle Airport (CDG) to Chicago O'Hare International Airport (ORD)
Depart: 10:40am
Arrive: 01:45pm
Paris, France (CDG) to
Chicago, IL (ORD)
Air France
Flight 3602 operated by Delta Air Lines
Economy Class
(on Boeing 767)