We study superconductivity states mediated by the BCS and Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairings in superconducting Weyl semimetals. It is found that a mixture of BCS and FFLO pairings results in a distinctive double-gap structure for superconducting states. With a heterojunction of a Weyl semimetal and a superconducting Weyl semimetal, we demonstrate the nonholonomic Andreev reflection and show that the intra- and internode Andreev reflections increase at the edges of the effective gap. The influence of interface potentials on the Andreev reflections is investigated. The conductance spectra arising from the mixed superconducting pairings is also analyzed.