hmm, major changes needed on names here, you have the parents listed as John Borrie and Marie Louise Bodway.
The couple married on 11 October 1858 in St-Patrice-de-Sherrington were named Jean Baptiste Barré, son of Jean Baptiste Barré and of Charlotte Simard, of age, and Louise Beaudin, minor daughter of François Beaudin and of Rose Marchand, all residents of that parish. https://www.genealogiequebec.com/Membership/LAFRANCE/acte/4831044 Marriage record IGD Drouin (membership)
Henry cannot be born 27 June 1860. His parents have a son named Emerie Barré, born on 30 June 1860 and baptized on 1 July in the parish they married in. Godparents for that child are his paternal grandfather and maternal grandmother. https://www.genealogiequebec.com/Membership/LAFRANCE/img/acte/5481774 Bapt. image IGD (Drouin)
Emery Barré married Célanire Langlois on 22 November 1881 in St-Valentin (St-Jean), so is definitely not your man. His parents however are listed on that marriage record as residing in the USA https://www.genealogiequebec.com/Membership/LAFRANCE/acte/5007902 Barré-Langlois marriage IGD (Drouin)
The location name you have for his birth is wrong, Québec is a city, the name as a province only applies after July 1st 1867.
There are other boys baptized with the name Henry Barry / Henri Barré in 1858 and 1860, but not with those parents.
Have you found him on a US census with his parents prior to his marriage?