A young man--we can sketch his portrait at a dash. Imagine to yourself a Don Quixote of eighteen; a Don Quixote without his corselet, without his coat of mail, without his cuisses; a Don Quixote clothed in a woolen doublet, ...; face long and brown; ... the maxillary muscles enormously developed, an infallible sign by which a Gascon may always be detected, even without his cap--and our young man wore a cap set off with a sort of feather; ....
There are two allusions in the third paragraph of the story (excerpt above) that give a good example of how Dumas uses clichés in this story. A cliché is an expression that is familiar within a culture. It has an agree upon figurative meaning that is different from the literal meaning. This agreed upon meaning is based in metaphor or analogy and expresses something that is deeper than the literal definition expresses. So far this sounds like an idiom, and idioms can be clichés. Allusions can also be clichés. Commonplace metaphors or similes can also be clichés.
What carries an idiom, an allusion, or a metaphoric phrase over to becoming a cliché is over use. At one time, Babe Ruth was the most renowned of all American baseball heroes. A common metaphor for young baseball players was, "You are a regular Babe Ruth." The culture understood that this metaphor meant the young person was a great baseball player. Then the metaphor grew to being a cliche because every parent and every coach of every boy or girl who picked up a baseball bat was told, "You are a regular Babe Ruth." Thus the metaphor became an idiom that became a cliché. Cliché really identifies the usage of figurative, non-literal, expression in several classes of things (e.g., allusion, idiom, metaphor) rather than identifying a separate class of expression.
Back to Dumas. In the second paragraph, he refers to the as yet unnamed young man as "Don Quixote": "Imagine to yourself a Don Quixote ...." This is (1) a literary allusion to Don Quixote by Cervantes and (2) a metaphor comparing this lad to a tilter at windmills (i.e., one who fights useless battles). He also refers to him as a Gascon, pinpointing his regional identity: "an infallible sign by which a Gascon may always be detected, even without his cap ...." The audience Dumas addresses knows precisely the qualities these two descriptions call to mind. We do not know because these have ceased to be relevant to our world, but the people in the setting of the story and the readers of the story did know. In fact, the humorous irony that accompanies Dumas's description ("of eighteen ... without his corselet" and "even without his cap") tells us that these allusions and metaphors are so often used and so well understood that they have, because of overuse, become clichés.
Finding other clichés in the story may be difficult because one of the defining features of a cliché is that its figurative meaning is culturally understood. But as you scan the text, after having read it and familiarized yourself with it, you will be able to recognize expressions that Dumas uses, like "Don Quixote" and "Gascon," that seem to mean something in context of the story even though the meaning escapes you. These might be cliché. You may also find expressions like the simile "love is a rose" that have carried over from earlier literary periods yet are still commonplace today, thus clichés by Dumas's time and still clichés in our time.