There is no boxing day in most of France (Alsace is the exception), including Paris. In fact, if xmas day falls on a Sunday, you are miss out of a holiday!
The French have xmas dinner late at night on xmas eve. So they go out and about on xmas day - a big contrast to the UK. If anything, Xmas day in Paris feels more like boxing day in London. Most of the big stores will be closed. Public transport runs a Sunday service (unlike London)
Sales are carefully regulated and will not start until a week or so into January. But I have come across some supermarkets sell off their toys cheaply on 22 or 23d December (very good for me, as I usually do my xmas shopping on the 24th). This is very annoying because I have a newphew whose birthday is on 2 january, and all the shops have stopped selling toys by then.