There were several West laceworkers inCalais in that period.
I have two Johns born c 1844 - on is John Walter Hart West born 27 August 1844 the son of John West & Mary Hart. living rue du Temple. and the other is John West son of john West & Annfrost born 29 August 1843, parents living rue du Temple.
John West & Ann Frost had five children while inCalais.
Have more details on these families if you have an interest. The family is most likely to have left Calais in 1848 - mass exodus during the revolution of that year.