Savoyard with Marmot, painted by Jean-Antione Watteau, in 1715-1716 now in the Hermitage Collection. The marmot is sitting on the box and the savoyard boy is carrying what is described as a flageolet, an oboe-like instrument. Looks like in some of the depictions of these itinerant musicians the box is a hand organ and sometimes they play other instruments and the box is for the marmot.
Here's a later print from a mid-19th century fancy dress plate. The female savoyard is holding a hurdy-gurdy. Notice that a distingishing feature of her costume is a cap that ties under the chin and an apron.
Also while rummaging around on the internet to see where one even acquires a hurdy gurdy these days I found this undocumented history of the street organ, and a fascinating TED talk by Caroline Phillips, "Hurdy-Gurdy for Beginners"