I can only relate my experiences and so I speak only for myself. The election of Pope Francis has made me want to be a better person, a better Catholic, and a more active Catholic. In the days leading up to his election, I prayed earnestly for the Holy Spirit to send us a Pope who was close to his people and who could help restore some of the trust that the Church has lost due to the various scandals. And so far, it looks like we have got the right guy- warm, humble, compassionate, down to earth, a love of the poorest, a man of deep service, a man who will clean house, and a man who leads by example.
So as a bad Catholic who really wants to be a good Catholic, I am delighted. It is not so much anything he has done as Pope- he has just been elected- but the example he has set by his behaviour over the course of decades. He actions, even the simplest of things like taking the bus and living among the poor, are a true evangelization, a true call to live as a servant, to answer my criticisms of others by improving myself, and to follow the Gospels in a very concrete way.
So as for my spirituality, the first things it has made me want to do is receive the Sacrament of Reconciliation, increase my daily prayer and readings, and get to as many Masses as possible during any given week. It has also made me want to do more on the ground- get involved in the Church in support of its charity and maybe, if I am good enough, make efforts to bring people back to the Church.
And my guess is that there are many like me- people with a basic Catholic formation, who have become somewhat discouraged, but who will come racing back with the least bit of encouragement and good example.
Thank God for Pope Francis.