In a scene at the 58min mark, Felicie tells a character, You're not my Mom! A gifted box containing a pair of orange or red ballet slippers on the kitchen table disappears as Felicie is seen leaving the kitchen to go outdoors.
When Félicie dances in a pub, an anachronism becomes apparent with the presence of the province of Quebec's flag. The film is set in 1879, while the flag design shown was not adopted until 1948.
The Statue of Liberty is shown as being already green when it should be brown. The bronze didn't deteriorate to green until around 1900.
A nearly completed Statue of Liberty and a half built Eiffel Tower are shown to be in Paris at the same time. In reality, the Statue of Liberty opened in New York in 1886, and the Eiffel Tower started construction only in 1887.
Félicie is shown wearing a pair of denim shorts over her leggings in many scenes. While it could be improvised and homemade (and is possibly implied to be, as it appears to be made from rolling up the leggings on a pair of jeans and sewing them in place with buttons), no one is known to have worn jeans in this manner prior to the 1950s when it became fashionable to do so.
Odette nicknames Félicie "Sherlock Holmes". The first Sherlock Holmes story was published in 1887 (possibly the year the movie is set) in an English magazine and wouldn't have been known in France until sometime after.
The movie seems to be set sometime between 1885 and 1889. While a motorcycle powered by an internal combustion engine was invented in 1885, Mr. Luteau's machine seems to be a design from 1895 at the very earliest.
When Odette is telling Felicie about Regine, she jokes that Regine likes to eat orphans with ginger ponytails (obviously referring to Felicie). However, Felicie's hair is in a braid, not a ponytail.