First, excuse the brevity of this fanpost. It's an idea I think others have had and not one that I have the time to fully consider (which only means input in the comments section will be awesome).
Francouer is built like a durable, major league starting pitcher. The first person I thought of when considering Jeff Francouer "The Pitcher" was Justin Verlander, and it's a pretty easy comparison to make. Verlander is listed at 6'5" 225lbs to Francouer's 6'4" 210lbs (according to baseball-reference), though I think we all know those numbers should always be taken with a grain of salt (the players get to just tell a dude their height and weight if I remember right?). But they should at least be in the same ballpark.
Next, and more importantly to consider, is whether the guy can actually throw the ball. As we all know, Francouer's arm-strength is the stuff of lore, like the Viking conquests of England or the blood dripping from Ghengis Khan's mustache. But the numbers seem to back it up as well. From Fangraphs, last year:
rARM- 8 (behind only Gordon and Torii Hunter; measures accuracy)
ARM- 8.6 (Best in baseball)
Arm Strength (87, according to Fangraphs scouting report; 10th best in the game)
Arm Accuracy (81, according to Fangraphs scouting report; tied for 11th)
How are the first two metrics calculated? No idea. But on the Fans' scouting report alone it's pretty suggestive that the guy at least has a pretty good arm. Jeff Francouer sucks as a hitter and has no range. At this point in his career, those two things are really unlikely to get better, outside of an occasional "blip" on the radar (read: fluke season). But he does have an actual ceiling to reach as a pitching prospect.
Convincing Francouer to go for it would be the toughest hurdle to climb. But if he has a season in 2013 remotely like he had in 2012, he's going to be completely out of a starting job...anywhere, and with little versatility in the outfield he makes for a poor bench player.