Hi Darren, I think your Achille was born in France or at least that's the place of birth given (probably by his father in law) in the 1861 census
Looking at your family tree, I found https://www.wikitree.com/wiki/Mahy-93 married to Emma Simms
Achille married Emma in Nantwich, Cheshire, in April 1860. The couple both gave their address as Hospital S[treet?]. Achille gave his occupation as a fitter. He gave his father's name as Louis, a soldier.
"England, Cheshire Parish Registers, 1538-2000," database, FamilySearch (https://familysearch.org/ark:/61903/1:1:F3PZ-NJG : 7 December 2017), Achille Mahy and Emma Sims, 17 Apr 1860, Marriage; citing item 1 p 211, , Nantwich, Cheshire, England, Record Office, Chester; FHL microfilm 2,105,032
The 1861 census entry (which I couldn't find on Family Search) has Achille and wife Emma living in Liverpool with Emma's parents. Her father, John Simms was a dock labourer who had originally come from Evercreech in Somerset. Emma and hers sister had been born in Bristol
Achille's birthplace is given as France. (link below to an freely viewable image on Ancestry)
https://www.ancestry.co.uk/sharing/21835796?h=6cae10&utm_campaign=bandido-webparts&utm_source=post-share-modal&utm_medium=copy-url
The 1871 census for Everton, Liverpool finds an Emma Mahy , born in Bristol with her children including Frank Mahy aged 3 months.There is no husband present
"England and Wales Census, 1871", database with images, FamilySearch (https://familysearch.org/ark:/61903/1:1:KZGT-B4L : 23 April 2019), Frank Mahy in entry for Emma L Mahy, 1871
Oddly the marriage register for Frank Mahy and Jessie Cox has his father's name written as Wm but that has been crossed out
https://www.ancestry.co.uk/sharing/21835834?h=f6ca6b&utm_campaign=bandido-webparts&utm_source=post-share-modal&utm_medium=copy-url
(haven't searched for Emma and Achille in any later censuses)