Most unusual name and nothing on FreeBMD for the Edouin family. There is however a William Edouin born circa 1860 on Genes Reunited. Perhaps there is some connection?
Wikipedia and several other websites all have a lot on him including early photos and the following.
Edouin, [William Frederick] Willie [né Boyer] (1846–1908), comic actor
Edouin was born in Brighton under the name William Frederick Bryer, the youngest of five children of John Edwin Bryer, an English dance instructor, and his wife Sarah Elizabeth (née May).
In 1871, he joined Lydia Thompson's burlesque company, as its leading male comedian, and met his future wife, Alice Atherton (1854–99). The couple had 2 daughters, Daisy & May,
So perhaps you should be looking under a range of names like Boyer or Bryer for hiim. His Brighton Birth cert is probably under Bryer in the March quarter of 1846 but his marriage could be under any of those names, probably in America where he spent much of his time.
Roy G