If a sparse language is NP-complete then are all NP languages sparse?
If we only consider the latter half of the question: "are all NP languages sparse", the answer is no. A counterexample is $\{0,1\}^*$. It belongs to NP but is not sparse.

However, you added a precondition: "a sparse language is NP-complete", and $A\rightarrow B$ is true if $A$ is false, so the answer depends on whether there exists a NP-complete sparse language. Since it remains open whether there exists a NP-complete sparse language, your question also remains open.