In the meaning of vespers, vêpres is a borrowing from French (since French was the official language of the church, there are many such ecclesiastical borrowings) and comes ultimately from Latin vesperas (accusative plural of vespera = evening) referring to the evening prayers. Latin Vesper referred to the evening star, Hesperus (Hesperos being the Greek cognate).
As for wasps, the name derives probably from an Indo-European root meaning web (relating to the weblike construction of their nests – les vêpriéthes). The same root gives English wasp and Latin vespa, and Jèrriais vêpre and French guêpe both descend from Latin (and the Jèrriais verb dgêper = to hover is probably an adaptation of the French word). Italian has retained the form vespa for wasp, hence the name of the buzzy scooters.
So wasps and vespers have ended up in Jèrriais in the same wordform from different starting points. But Dgèrnésiais has paemperluche (or paepernuche, paeperluche, pimpeluche…) for wasp – but in Jèrriais pîmpèrluche is a dandy or fop!