The microscopic structure of Na+-doped helium clusters (Na+. He-N) is investigated by employing the path integral Monte Carlo (PIMC) method. Our primary interest is in determining the nature of superfluidity in these clusters by examining the temperature and size dependences of several physical quantities such as energy and superfluid fraction. Comparison with Boltzmann statistics has also been made to clarify the effects of superfluidity. It is found that clusters of N greater than or equal to 100 have a triple-layer structure where the first shell is rigid-body and solidlike and the third shell is almost like liquid helium. Between T=1.0 K and T=1.25 K, a superfluid transition is observed in the second shell. This transition temperature shifts to a lower temperature than that observed in bulk liquid helium because the finite system size and strong binding to the cation cause superfluidity to be suppressed. By computing the effective moment of inertia as a function of cluster size, it is found that there exists a specific number of helium atoms needed for the formation of the complex, the components of which are in a state of normal liquid.