According to this CNS article, Pope Francis will not be like his predecessor when it comes to chant. Emphasis mine:
After a musically proficient and polyglot Pope Benedict XVI, it came as a surprise to many that Pope Francis doesn't sing or chant at Mass or speak foreign languages in public.
From his first Mass as pope -- his liturgy with the College of Cardinals in the Sistine Chapel March 14 -- the pope has not chanted or sung during the usual moments of the liturgy, such as before the eucharistic prayer.
His ditching any musical pitch was even more evident during the "Regina Coeli" April 1, when he spoke, rather than intoned, the Marian prayer.The article goes on to say it could be because of Francis' "husky" voice, or the Jesuit maxim of "nec rubricat, nec cantat," or sloughing off the rubrics and the chant.