You'll find taxi stations at airport and train station exits.  Tell your driver to take you to 8 rue Chambiges in the 8th district.  Or ask the hotel's concierge to arrange for a chauffeured car to pick you up or take you back to the Orly or Roissy-Charles de Gaulle airports.  (The trip costs € 96 one-way in either direction). 
 
From the Alma Marceau Metro station (line 9), take the exit marked "Place de l'Alma".  Once outside, stay on the left side of Montaigne avenue and turn left onto Clément Marot street, then left again onto Chambiges street.
 
From the Franklin D. Roosevelt Metro station (lines 1 and 9), take the exit marked "Avenue Montaigne" and stay on the right side of the avenue.  Then turn right onto Clément Marot street and left onto Chambiges street.

From the Orly and Roissy Charles de Gaulle airports:

You can take an RER train into the city from either of these airports.  Take the RER-B line to the Châtelet les Halles station and then change to Metro line 1 (Direction "La Defense") and get off at the Franklin D. Roosevelt station.

By car from Roissy Charles de Gaulle airport (25 km): 45 minutes.

Take the "A1 Sud" motorway and head for Paris.  At Porte de la Chapelle, take the Boulevard Périphérique Ouest and exit at Porte Maillot.  At the roundabout at Porte Maillot square, take the Avenue de la Grande Armée and follow it to Place de l'Etoile (Arc de Triomphe).  Then take the Champs-Elysées and turn right on the third street--Avenue Georges V.  Go left on the Rue du Boccador, and Rue Chambiges will be the second street on your left.

By car from Orly airport (18 km):

Take the "A6 Nord" motorway headed for Paris.  At the Porte d'Orléans, take the west ring road ("Boulevard Périphérique Ouest") until you reach the Seine River.  Then take the first exit to the right after crossing the Seine on the Pont du Garigliano bridge, and follow the quays to the Pont de l'Alma.  At the Pont de l'Alma roundabout, go three-quarters of the way around and get on Georges V avenue.  Turn right on the Rue du Boccador.  The rue  Chambiges will be the second street on the left.  The nearest parking garages are the Parking Georges V on Georges V avenue, and the Parking François 1er on François 1er street.

From the Gare du Nord (Eurostar / Thalys trains):
Take the RER-B line to the Châtelet Les Halles station.  Then change to Metro line 1, (Direction "La Defense") and get off at the Franklin D. Roosevelt station.

From the Gare de l'Est:
Take Metro line 4, direction "Porte d'Orléans" to the Châtelet Les Halles station.  Then  change to Metro line 1, (Direction "La Defense") and get off at the Franklin D. Roosevelt station.

From the Gare de Lyon:
Metro line 1 (Direction "La Défense") is direct to the Franklin D. Roosevelt station.