At the end of the film at the hospital, there is a statue of St. Therese of Lisieux. The Exposition took place in 1889, eight years before Therese died, and she wasn't made a saint until about 1925.
In the opening scene, an advertisement for the Paris Exposition Universelle states that it will be open from May 6 to November 6, 1889. Actually it closed on October 31, 1889, and the closing ceremony was held on November 6, 1889. The advertisements before and during the exposition were as stated above.
Incorrectly regarded as a goof - Police is spelled the same in French and English, so the station sign is correct.
Much of the language, both written and spoken, in Paris is in the native French as it should be. However, the sign for police station outside the building is in English.