The Eurostar is your best bet. It takes about 2.5 hours and arrives in the city. Book tickets ASAP.
To navigate the city efficiently, buy a Mobilis Day Pass (5.50E) when you arrive at Gare du Nord (or any other ticket window in a métro station). It covers all public transport for the day.
Correction: Mobilis Day Pass is 5.60E
Depending on when this will be, you might be able to get an inexpensive promotional fare from Eurostar. I would certainly recommend the train rather than a plane, because it takes a lot less time counting the need for early arrival at the airport for security, etc., and it goes from city center to city center so avoids costs and time for getting to/from airports. You can buy tickets three or four months in advance, and the sooner you buy the better your chance of a good fare (do it on line - generally much less expensive than Eurail or similar sites).
From the station in Paris (Gare du Nord), take the Metro to the center of the city and just walk around. You can get almost anywhere you would want to visit on foot, and that also will allow you to see a lot. (Sounds like this would be strictly a day trip? If so, the Metro will be really easy because no luggage, etc.)
Other alternatives would be a trip along the Seine by boat, or take a "hop on, hop off" bus tour. Even if you're there for only a day, that's time to walk around and get a bit of a feel, visit Notre Dame or Sainte-Chapelle or the Arc de Triomphe (great views of the city from the top), etc., and still spend some time in a cafe just watching people.
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