The answer to the question of how long Canis familiaris, specifically Basset Hounds, will live, is entirely dependent on care of the animal, starting with, not just the immediate family, but preceding generations. Proper medical treatment by qualified individuals, proper diet, and proper habitat (even if this includes habitation within a home and little outdoor exposure), is vital to the longevity of these animals.
Because this is a breed bred almost exclusively for hunting purposes, it would stand to reason that moderate exercise would necessitate a healthy lifestyle, thus increasing their longevity. This should be coupled with moderate amounts of fresh, clean water, especially during exertion such as exercise (water should always be available to a dog). Be certain to ask a veterinarian or other qualified individual about exercising a pet, as this can depend on their health and other factors.
According to current surveys in the United Kingdom, where this breed is common (it is believed to be of French origination through tapestries of hunting and mention in texts throughout the Middle Ages and earlier, even down to its French namesake), Basset Hounds range in longevity from 10-20 years. However, the populations surveyed are rather small, and can also be from hunting stock, which can be of differing lifestyle and lineage than modern pet Basset Hounds.
Sources and Further Reading:
 Basset Hound Club of America (BHCA)
* The Complete Poetical Works of William Wordsworth By William Wordsworth, John Morley, Walter Scott, 1890
* The Dogs of Folklore By Richard John King 1874
* The Social History of Great Britain, During the Reigns of the Stuarts, Beginning With The Seventeenth Century, Being The Period Of Settling The United States By William Goodman 1847
* Advances in Veterinary Science and Comparative Medicine By Charles E. Cornelius, Charles F. Simpson, André G. Rico
*The Complete Home Veterinary Guide By Chris C. Pinney