Class Field Theory states the correspondence between abelian extensions of k and congruence divisor class. In idelic language, there is a surjective map from $J_k/k^*$ to $Gal(k^{ab}/k)$ with its kernel unkonwn.

Tate's Thesis proved some functional equations and analytic continuity(with a finite character of $J_k/k^*$).

Question: Why Tate's thesis contributed to class field theory?

on the adelic side. But class field theory is needed to connect those with the Galois side, so one could say that class field theory plus Tate's thesis tells us analytic facts about $L$-functions attached to characters on Galois groups or Weil groups. In that sense they are closely related, but neither logically depends on the other. (See Tate's own description of necessary background in his thesis!) $\endgroup$ – Boyarsky Jun 22 '10 at 17:22