Say the word "Paris" to someone, and they'll probably conjure up a knee-jerk image of, say, a romantic sidewalk café and people in berets drinking coffee. Eustacia has this reaction, only a hundred times more intense. For her, Paris represents everything she wants out of life: luxury, adventure, culture, and romance.
A young and clever man was coming in to that lonely heath from, of all contrasting places in the world, Paris. It was like a man coming from heaven. [...] This was the obscure, remote spot to which was about to return a man whose latter life had been passed in the French capital – the center and vortex of the fashionable world. (2.1.28-31)
[S]he had represented Paris, and not Budmouth, to her grandfather as in all likelihood their future home. Her hopes were bound up in this dream. In the quiet days since their marriage, when Yeobright had been pouring over her lips, her eyes, and the lines of her face, she had mused and mused on the subject, even while in the act of returning his gaze. (4.1.4)
We can really see the disjunction present in Clym and Eustacia's relationship here. When she sees him, all she can think of is Paris; he's sort of like a means to an end for her. Clym, meanwhile, is extremely physically attracted to Eustacia.
So "Paris" the word represents a whole host of longing and desires for Eustacia. Paris greatly contrasts to the heath, which is why Eustacia longs for it so darn badly. As such, it also represents the entire outside world, particularly the more modern and urban world Eustacia longs to join. Paris, for Eustacia, represents the entire world outside the heath.
This makes Clym's return from Paris all the more interesting – we can see how Clym, returning from the "wider world" makes Eustacia fall in love with him. And we can also see how the reality of Clym and Paris causes a lot of grief for Eustacia, who had been clinging to a dream world, represented by a Paris that never really existed in the first place.