I would like to think that St Francis saw Jesus as our Redeemer. One who went on the cross for his children and for love of them, died so as to reconcile us back to the Father. And I think that St Francis recieved the Stigmata mainly because he grew so much in his love for God that he began to identify himself with His Savior.
St Francis is a great example of charity in all that he did for the poor and in helping those who had fallen away from the Church (or who had been separated from). Since he did all of these out of love for Christ, he identified with Jesus's greatest example of self-giving.
"Greater love has no one than this, that one lay down his life for his friends." (John 15:13)