As modern as it sounds, Blaise is an ancient Christian martyr name,and also in Arthurian legend the name of Merlin the Magician's secretary. Its relation to the word and name Blaze gives it a fiery feel. Amanda Beard named her baby boy Blaise Ray.
Saint Blaise, an Armenian bishop, is the patron saint of wild animals and those with sore throats. Blaise Pascal was the seventeenth century French mathematician-physicist-inventor-writer-philosopher among whose many accomplishments was the invention of the calculator. And in the modern world, Blaise Zambini is a minor character in the Harry Potter franchise.
Blaise has been on the lower rungs of the popularity ladder since 1996, while Blaze ranks somewhat higher.