Beauty and the Beast was originally a French fairy tale written by Gabrielle-Suzanne Barbot de Villeneuve and published in La jeune américaine, et les contes marins in 1740.
An abridgement was published in 1756 by Jeanne-Marie Le Prince de Beaumont, in Magasin des enfants,
ou dialogues entre une sage gouvernante et plusieurs de ses élèves , with an English translation appearing in 1757.
This places the story in the mid-1700s.
Both rifles and steam-powered machines had been invented by that time, so their inclusion in the story would not be anachronistic.
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It would at least be 1800 as the matches that Lumiere uses in be our guest were not invented until that time period.
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In the Disney movie, the Eiffel tower is shown (during the song "Be our guest"), however construction of the Eiffel tower wasn't until the late 1880s, so it could have been set around then
(or else it's sloppy work by Disney).
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In his tour Cogsworth refers to both the baroque period (1585-1700ish) and rococo period (1700-1770ish), and based on the costumes and hairstyles
it could be as early as 1730 or as late as 1870 (excluding about 1780-1830).
Factoring in the technology, 1840-1860 is the most likely answer.
The fact that the beast is called a prince is questionable, but he clearly doesn't rule any kind of kingdom, and seeing as his castle is rather hidden in the countryside his family may have escaped the ravages of the revolution.
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If you discount magical musical production numbers showing yet to be built iron work towers as evidence and only look at technology in use, clothing styles, and political sensibilities it very easy to realize it is set late 1790s up to early 1800s.
steam powered machines exist they are pretty rare and mostly used in factories but the whole piston mess Maurice has going has existed since 1712 Gaston's gun is a blunderbuss which would be in use till the mid 1800s but by then there were much better guns.
both Gaston and Beast wear tailcoats which don't exist till the 1790s Belle (not counting the yellow ball gown) and
the other young ladies don't wear big poofy dresses instead
their skirts look more like empire dresses.
all the towns people seems to have zero qualms about storming a castle not something you would do if you know the royals have the power to throw you in prison, something they don't have after the French Revolution, 1789-1799.
no one seems to be missing a prince who is hiding in a remote castle in the mountains
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I agree that it occurs in the mid 1700s because after 1789 there is no monarchy in France
so the Beast wouldn't be royalty if the movie/book occurred after the French Revolution.
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The 1991 disney adaptation of  Beauty and the Beast , we see several references to technology that seems out of place with the setting, including rifles and steam powered machines. It makes it hard for me to try and judge when the film would be set.   Is there any official answer, on when the film is mean to be set?
What time era is the Disney version of Beauty and the Beast meant to be set in?
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<plot-explanation><beauty-and-the-beast>
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Beauty and the Beast  was originally a French fairy tale written by Gabrielle-Suzanne Barbot de Villeneuve and published in  La jeune américaine, et les contes marins  in 1740. Later on An abridgement was published in 1756 by Jeanne-Marie Le Prince de Beaumont with an English translation appearing in 1757.  This places the story in the mid-1700s.   The story is in the mid-1700s.
Beauty and the Beast was originally written by Gabrielle-Suzanne Barbot de Villeneuve in 1740. An abridgement was published in 1756 by Jeanne-Marie Le Prince de Beaumont. An English translation appeared in 1757. This places the story in the mid-1700s.