What does canapé en corbeille mean?

It refers to a basket-shaped frame. The back curves around smoothly in a continuous line to meet the armrests without any sharp corners. This form became popular in the eighteenth century. Sitters found the curved ends comfortable for resting against while turning to face someone else.

How to date a French sofa?

Start by looking at the leg shapes. Straight, fluted legs point to the late eighteenth century, while curved cabriole legs indicate earlier decades. The carving also helps. Symmetrical geometric patterns suggest later neoclassical tastes. Asymmetrical floral work usually means an earlier frame. Check underneath for circular saw marks. Hand-sawn timber in the hidden carcase is a good sign of age.

I bought this old sofa and it has a really low back compared to normal ones. Was it made for a specific room or purpose originally?

You are likely looking at a piece built to sit beneath a window. Tall backs block natural light, so makers designed low-profile seating for exterior walls. They also sat in front of large mirrors. The low back allowed the mirror glass to remain visible, reflecting light back into the room. These are sometimes called confidantes if the ends are partitioned off. The low height keeps the room feeling open.

The fabric on the arms stops halfway back and leaves exposed wood. Is this just missing upholstery or was it actually designed to look like this?

That is an intentional design. The small upholstered pads on the armrests are called manchettes. They provide somewhere soft to rest your elbows while keeping the carved wooden arm supports visible. If the fabric ran all the way to the back, it would hide the timber joints. French menuisiers wanted their carving seen, so they rarely covered the entire arm.