Start by doing what’s necessary; then do what’s possible; and suddenly you are doing the impossible.
This saying is widely attributed to St. Francis (e.g., by Nancy Pelosi in the Congressional Record for April 26, 2006, of all places), but it sounds like him only if your idea of St. Francis is a 13th Century Zig Ziglar. In other words, it fails the “sounds right” test.
A basic Google search for it turned up the usual suspects (brainyquotes, goodreads) and this blog post from a Franciscan who thinks it’s not by Francis either. Wikiquote has it on their “removed for lack of a source” list. It was placed on that list in 2010 and no one has come up with a source since.
I searched Google Books for it and the oldest hit I found was (I am not making this up) the Fall 1993 issue of Jewish Communal Service. From what I can see in the search snippet, they quote it as a well-known saying, so there is likely a source before then, but I can’t find it.
I checked all appearances of the word impossible in the EWTN copy of The Little Flowers of St. Francis (yes, I checked the pages linked from that page too) and didn’t find it.
I can find no evidence that St. Francis said it and therefore confidently say that it is a fauxtation.