Hard Times by Dickens and Hard Times by Stephen Foster were both published in 1854 - which would indeed suggest that, since it takes longer to write and publish a novel than a song, it couldn't have been a case of Dickens borrowing Foster's title. There is a character in Dickens novel called Foster, but I doubt if that is significant.

But there's nothing in the song that suggests any borrowing or inspiration other than the name itself - and that could just as easily have come from "Oh the Hard Times of Old England", which is probably where Dickens took it. I've always understood that to be from the immediate post-Napoleonic period.

The Roast Beef of Old England is very much pre-Kipper. Hogarth's painting with that title is dated 1748. And this site gives the date of the song as 1735. I don't know when the French started calling the English "les Rosbifs", but I suspect round that time.