Despite what their common surname suggests, they were not related closely by virtue of both being Stewarts — being only ninth cousins once removed in the male line.
It was rather through their shared grandmother, Margaret Tudor (daughter of King Henry VII of England) that they were related, and which gave both their claims to the English throne.
The later English kings and queens of the House of Stuart, from James I and Charles I onwards, were more properly members of the Stewart of Darnley branch, and all drew upon their feudal heritage in Lennox.
For his services, he was rewarded with the lands of Aubigny-sur-Nère and Concressault, which were given to the second son in the family so they could live in France to strengthen the Auld Alliance.
By marrying Darnley, Mary neutralized a dangerous rival claim to the throne of England whilst strengthening that of her own house.