This paper studies geometric influences in product spaces of continuous distributions. Gaussian analogues of two of the central applications of influences, namely, Talagrand's lower bound on the correlation between increasing subsets of the discrete cube and the Benjamini-Kalai-Schramm (BKS) theorem on noise sensitivity, are proved. The proofs are based on the Ornstein-Uhlenbeck semigroup theory as well as approximation of the characteristic functions of monotone sets by smooth functions from functional counterparts. Analogous issues for discrete product probability spaces are also discussed. \par \{For Part I see [N. Keller, E. Mossel and A. Sen, Ann. Probab. {\bf 40} (2012), no.~3, 1135--1166; 2962089 ].\}