In the 1800's France was still a patchwork of regions with different customs and where spoken French was not even uniform with many areas still keeping to their local dialects and customs.
Christmas celebrations did not solely focus on December the 25th. Effectively it was a sequence of varied celebrations that surrounded the winter solstice and there was a wide variety of local customs which prevailed depending where you lived. Christmas eve/day in France, apart from the period of the French revolution when Christian festivals were banned, was essentially a religious occasion. People went to midnight mass and since the journey could be difficult, long and cold, they had a meal called "réveillon" either before the service or after getting back home. The exchanging of presents was actually linked to Twelfth Night which was the date when the three kings were said to have arrived in Bethlehem bearing gifts and, for a long time this was a special day, with a celebratory meal in the evening at the end of which a special cake called "galette" was shared. A dried bean was hidden in it and the person who found it in his or her portion was made 'king' or 'queen' for the evening and was entitled to send others on fool's errands or make them do unusual tasks. When the "king" raised his goblet everyone shouted "Le roi boit" and there was a great deal of laughter as he drank and spluttered. Presents were also exchanged or drawn from a bran tub. These customs went back to medieval times. Nowadays only the tradition of the galette still survives on twelfth night and it is an ordinary day.
In the north of France, the major celebration for children was Saint Nicolas day on December the 6th. They left their shoes or clogs in the fireplace and the saint came down the chimney with his assistant and his donkey. It is he, of course, who subsequently became Santa Claus in the USA, who also calls during the night and leaves presents under the tree on Christmas eve. In the 1800's the presents that the children would get would be very simple: a peg or rag doll, a carved toy, a spinning top, a whistle, a hollowed out wooden egg with something smaller inside, and perhaps a few sweets or sugared nuts. Sugar was mostly made from beet at the time and was a luxury in those days. A child who had consistently misbehaved found a piece of coal, a cane or a small whip in his shoe/clog. In richer families children had special almond biscuits in the shape of Saint Nicolas with icing on top, or fruits made out of coloured marzipan.
The Christmas crib originated in Italy and was first introduced in churches there by saint Francis of Assisi in medieval times. It spread throughout southern Europe. The original idea behind the santons representing ordinary people like the mayor, the poacher, the goose girl, the wood cutter, the fishmonger, the milkmaid, etc...was to make an effigy of a person that could not be present at the time, or go to mass, and it was placed by the crib to represent the absent person. After that people were rather charmed by the idea and adopted the custom of the "crèche" in their home, some of them with quite a few additional characters besides Joseph, Mary and the babe, and it became handy during the French revolution as they could celebrate privately. The area of Provence where the santons are still made nowadays is near Italy, but in the mountains and other parts of France people whittled their own figures from wood and you can still see some of them in the museums of other regions like Alsace or Burgundy. Some of the main characters in cribs displayed in private homes were also sometimes made out of spent wax in convents by nuns.
In Alsace and Jura the Christmas tree was brought in for good luck then decorated, and in many parts of France mistletoe, which was an ancient Gaul druidic New-Year ceremony plant, and holly, were used for decorations over the Christmas period.
In Provence, where it is warmer, there were outdoor processions and shepherds would bring their sheep to the church and carried a lamb in to be blessed. There was a live crib in the church with a real baby. In the North children made lanterns out of carved beet and went round their neighbourhood singing a traditional Christmas song (but not a religious carol) to get a few coins thrown at them.
Obviously people of different classes and backgrounds also celebrated according to their own means. Many drank beer, or, in regions were no grapes grew, home made wine made from other ingredients than grapes in the spring or the summer. There were also special Christmas foods, biscuits like "craquelins" made out of puff pastry in the shape of a baby, and cakes made out of ingredients preserved, dried, or saved during the summer.
I did research on Christmas traditions in France as part of a comparative study on European traditional customs.