The term you are looking for is bourgeoisie, not bourgeois.
Marx used bourgeoisie to describe the capitalist class. "Bourgeois" is a term that describes a class of people pursuing hedonism and/or materialism.
The bourgeoisie are not homogeneous. There is the haute bourgeoisie vs. the petite bourgeoisie.
Marx was quite specific on what he meant by bourgeoisie and they were truly the middle class: the go-betweeners between the nobility and monarchs and the peasants. Bankers, business owners in towns and cities, etc. The true owners of the means of production.
Full text and translation from German to English, is here (I've linked the relevant section):
https://en.wikisource.org/wiki/Manifesto_of_the_Communist_Party/1
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