Of Englishe Dogges
The Diversities, the Names, the Natures, and the Properties
Published in 1576 this is the first book to mention the various English breeds. It makes few references to topics that interest us here, however it does show that imports of French breeds did happen as early as the 14th century.
Of Englishe Dogges was originally published in Latin, but you can read an English translation at archive.org (see sidebar).
The citation below (taken from the English translation) may refer to the Basset Bleu de Gascogne
or its ancestor, the Grand Bleu de Gascogne
There is also at this day among vs a newe kinde of dogge brought out of Fraunce (for we Englishe men are maruailous greedy gaping gluttons after nouelties, and couetous cornorauntes of things that be seldom, rare, straunge, and hard to get). And they bee speckled all ouer with white and black, which mingled colours incline to a marble blewe, which bewtifyeth their skinnes and affordeth a seemely show of comlynesse. These are called French dogges as is aboue declared already.
Basset Bleu de Gascogne