MLB Rule 2 defines a foul ball and includes the following ...
"A batted ball not touched by a fielder, which hits the pitchers rubber and rebounds into foul territory, between home and first, or between home and third base is a foul ball."
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It's a fair ball as long as that's where the ball lands. But, it doesn't matter anyway because all players are supposed to be in fair territory to play.
Clarification
If a ball is touched like the scenario you have painted above. It does not matter where the ball lands. The determining factor to whether it is fair or foul is where the ball is in relation to the foul line when it is touched --- if the ball is in the air in fair territory and you touch it making it land in foul territory... this is fair ball since the fielder touched it when fair territory and visa versa -----tigersy2k3