1. Francis of Assisi did not say it, and
2. It is not biblical.
"Preach the gospel; use words if necessary" goes hand in hand with a postmodern assumption that words are finally empty of meaning. It subtly denigrates the high value that the prophets and Jesus and Paul put on preaching. Of course we want our actions to match our words as much as possible. But the gospel is a message, news about an event and a person upon which the history of the planet turns. As blogger Justin Taylor recently put it, the Good News can no more be communicated by deeds than can the nightly news.
Many have noted how Francis modeled his life on Jesus. But it wasn't just about the life of poverty, but also the life of preaching. We have no instance of Jesus performing a miracle and not speaking a word of comfort or challenge afterwards.
Paul articulated succinctly what Francis and Jesus felt in their souls: "How are they to call on him in whom they have not believed? And how are they to believe in him of whom they have never heard? And how are they to hear without someone preaching?" (Rom. 10:14).
To be sure, words used cheaply, thoughtlessly are worse than no words at all. As Westmont College professor Marilyn McEntyre says in an essay in the upcoming August issue of Christianity Today, "In an environment permeated with large-scale, well-funded deceptions, the business of telling the truth, and caring for the words we need for that purpose, is more challenging than ever before."
That being said, a better saying (which you can attribute to anyone you like) is this: Preach the gospel—use actions when necessary; use words always.
HT: Khalid bin Malek