There were certainly many British workers in France working in fields such as iron forging and in the railways. They weren't sent over as apprentices - and if he was 37 in 1851 then during the 1840s he was too old for any formal apprenticeship.
Rather, they were brought over because they had skills that weren't available locally at the time. In many cases British investors/owners were involved and sometimes large groups of men were brought over from towns in places like Staffordshire. Most eventually went back (when the local talent was trained up).
There was no requirement at this time for the registration of British children born overseas. They could have been recorded in the French records (in which case it would help to have some idea of where they were from, perhaps from later census records for William and Thomas if available), they could have been baptised in a British Chapel in France if one was nearby to where they were living, or have been baptised only when the family came back from France.