What's a word for someone who likes the finer things in life - classy taste, but makes do and replicates that expensive taste with cheap things?
While not limited to affecting expensive trappings, the term poseur (or poser) is often used to mean
a person who assumes attitudes or manners merely for their effect upon others
It also may not reflect a true appreciation for quality, but merely the impression it conveys.
[Collins American Dictionary]
A related concept is veneer of respectability. One of Macmillan's definitions of veneer is
a pleasant appearance, or a polite way of behaving that is not sincere: a veneer of respectability
Again, this is not limited to luxury goods.
Cheapskate implies someone who always find ways to pay less or as little as possible, but does not imply poor, and would often be used towards someone who has means, but still wants to spend like a tightarse.