When you mentioned ironworker I did some digging and found the answer to why the family went to France and where they went - Charenton. I'll go look at the Charenton records again.
In the early 1820's Aaron Manby took over the running of the Charenton Ironworks near Paris. He was an ironmaster from Birmingham who had fabricated an iron steamship at his Horseley Ironworks in 1822. The parts were then sent down the Thames to Rotherhithe to be assembled. The steamship was named Aaron and made it's début on the Thames in June 1822. A few days later it sailed to Paris. The Charenton Ironworks were so successful that another was opened at Chaillot.
At the time the English were superior to the French in iron-working so Manby recruited several hundred English workmen to come to France with the promise of good wages.