These are two kinds of armchairs, one upholstered on the sides (the bergere) and one open on the sides (the fauteuil).
FAUTEUIL is pronounced "foe TUR" and is an open-sided armchair. Here are a pair of late 17th century Baroque Italian fauteuils upholstered in C. Mariani 22k gilded leather:
Many antiquarians pronounce fauteuil "foe TOY (yuh)" and only use the term when discribing big, important armchairs that aren't upholstered on the sides. There's no right or wrong on this weird word, so don't sweat it. I just say "armchair" and skip the French but if you say "foe TUR", any antique freak will know what you mean. Wait. Wouldn't that be a great name for a new antique blog: Antique Freak. I love it!
Anyhow, here's another pair of fauteuils, these upholstered in C. Mariani's hand dyed and antiqued "Cinnabar" leather. This pair is 18th c. Italian Louis XVI (neoclassical style):
List price: $131,500 USD, the pair
And here's a third pair, again 18th c. Neoclassical Italian Louis XVI walnut and now upholstered in our 22k gold leafed leather:
List price: $107,000 USD, the pair
Now let's turn to the BERGERE.
A bergere is another type of armchair, this one upholstered on the sides. It's pronounced "behr ZHAIR" and people also just call it a club chair.
Here is a late 18th century Directoire bergere (pronounced: "direct TWAHR"; the Directoire period in France was from 1793-1799 and in the Neoclassical style but very simplified):List price: $12,100 with losses and restorations
Here is another bergere, this one a 19th c. European ("French") walnut Austrian Biedermeier (pronounced "BEAD" uh mire" and this style lasted from 1815 to 1848):List price: $20,000 USD
And lastly, a third bergere, this one 19th c. French Burl Walnut Charles X (the period just after the Empire, 1815-1834 and still in the Neoclassical style) upholstered in C. Mariani glazed leather:
List price: $14,000 USD