A pdf preprint of the article Newfoundland and Labrador: A mosaic founder population of an Irish and British diaspora from 300 years ago is posted in BioRxiv. The lead author, Edmund Gilbert, is well known for his studies of geographic distribution and linkages from DNA data.
Analysis of 1,807 Newfoundland and Labrador individuals shows English ancestry is predominant except for Irish in the south and south-east. A genetic bottleneck exits approximately 10 to 15 generations ago.
These findings are consistent with the isolation of outports and known genealogical evidence. The comparative genetic data to establish DNA connections to French (and Spanish?) settlers is not available, nor is that of the indigenous populations.