Franciscan study has always been a thorny issue. There is Francis himself, in chapter X of the Rule: "let those who don't know how to read not be anxious to learn." That would seem to dispense with the question of learning, and perhaps it's this streak in the Franciscan tradition that has kept it from being identified closely with scholarship in the fashion of the Dominicans or Jesuits.
We must notice the context of Francis' statement, however. This section of chapter X is about the danger of vainglory and pride, not about scholarship. Ever since St. Paul the Christian tradition has known that knowledge carries with it the tempation to these sins. Francis' concern is that his brothers and sisters maintain the minority of humility. With these, they can engage in any work suited to the life. Without them, it doesn't matter what they do.
As far as sacred or theological study goes, in his Testament Francis himself commands us to venerate all theologians.
The Capuchin Franciscan Constitutions of 1536 offer a prayerful exhortation to be made to students before each lesson:
Lord, I am the lowliest of your servants, unworthy of anything good, but I wish to enter and see your treasure. May it please you to let me come in, unworthy as I am, and grant that, through these words and holy reading, I may not only learn about you, but learn to love you, for I wish to know you only so that I may love you, my Creator, my Lord and my God. Amen.
So long as the end of our learning is the love of God, and we remember that the treasure of knowledge is not our own, but belongs to God and that we are studying for the sake of the service of those for whom we are learning, we will be well on our way to becoming genuine Franciscan students.
Update: Today one of the friars supplied to me the original Latin of the prayer above, which I had never seen. I was struck that the word translated "lowliest" is vilissimus, from vilitas, from which we derive "vile" in English. This recalls also the Rule in which the friars are admonished to vestimentis vilibus induantur, to be dressed in cheap clothing.