A possible alternative origin for the Morrells in the Thirsk area has occurred to me, though it's pure speculation and I have no evidence for it.
Between Darlington and Richmond there's a village called Newton Morrell. It's mentioned in the Domesday Book, and it's generally reckoned that Morrell derives from the Norman surname. Is it possible that Normans gave their name to the place, and that later folk, who had no direct male-line descent from the Normans, used the place name (or part of it) as their own surname some 400 years later? Just a thought.
I have a copy of a printed transcript of Thirsk registers, and there's no mention of France in the place index, nor do the surnames include more than a handful of names that might be of French origin.
The occupations do include a number of textile-related trades, however. I'm currently looking at a family involved in the wool trade where there's fairly strong evidence that they moved from Norfolk to Yorkshire in the first half of the 16th century, so it's possible that others made a similar move, and from other parts of the country. In pre-industrial times, my impression is that the wool trade spread out across the whole county, rather than being concentrated in the West Riding.