"享有市民权的人" can be translated into English as "people who enjoy civic rights" or "individuals with citizenship rights".
"Civic rights" generally refer to the rights and privileges associated with being a member of a particular city or community, though it can also be used more broadly to refer to rights within a nation.
"Citizenship rights" more explicitly refers to the rights and responsibilities that come with being a citizen of a country, which often includes local municipal rights as well.
Both phrases convey the idea of individuals having certain legal entitlements and privileges within a society. The choice between them may depend on the specific context and the emphasis one wishes to place on the nature of the rights in question.