To weaken France's image, to sow chaos, to get security forces focused on other things while they try to get specific targets.
There have been reports about both Russia and Iran being potentially involved.
So far I've seen an article about a Russian getting arrested 2 days ago.
They outlawed private DNA testing. As the article you linked to points out and explains.
And there's plenty of research that shows all Jews share a common genetic lineage to other groups in the middle east like Syrians and Lebanese.
One example: Jewish and Middle Eastern non-Jewish populations share a common pool of Y-chromosome biallelic haplotypes