So if you are offering your gift at the altar, and there remember that your brother has something against you, leave your gift there before the altar and go; first be reconciled to your brother, and then come back and offer your gift. (Matthew 5: 23-24)
Positively, we can say that it is living in a reconciled, fraternal way that makes us fit to offer sacrifice to God.
But the relation between the two things is even tighter than this. For what do we offer when we are at Mass but our own desire and efforts and loving our brothers and sisters and the sacrifices we make for them, uniting our own sacrifices to the one Sacrifice of the Lord?
In fact, everything that comes from the desire--itself a gift of grace--to be reconciled to our brother or sister is itself a sacrifice acceptable to God, an imitation of the Lord himself who allows himself to be tortured and killed that the world should be reconciled to God.
St. Francis is a model and pattern in this. For it is the same Francis who called the group that gathered around him a fraternitas as it was who adored Jesus Christ poor and crucified. His genius is the realization, in his life, that the two things must go together. Indeed, in communion with God in Christ, they become the same thing.