In drawing this connection, I learned some things, the first of which is the identity of the woman in this portrait by Jacques-Louis David (whose history paintings are a dominant presence in the Louvre). Her name was Jeanne Francoise Julie Adelaide Recamier.
Madame Recamier was considered to be the most beautiful woman in her day, and she influenced French art and literature. She was admired for her beauty, intelligence, kindness and graciousness, and was always surrounded by prominent geniuses who adored her good company. Here is an interesting short biography I found about her on-line: http://www.historyswomen.com/moregreatwomen/MadameRecamier.html
Now, the "Couch" as it is titled at the Carnegie Museum of Art: This is a chaise lounge, but is also described as a neoclassical "recamier" -- which is the woman's name in the David painting! (This particular neoclassical recamier was made in America in 1825.)
Link to detailed description of this couch from the Carnegie's web site: