Friar Laurence's plan was impractical and improbable from the beginning. In Act III scene iii, Romeo has been banished but is whining about having to leave, despite the fact that he is the one who committed the murder and should have been sentenced to death.
Here is what the friar says to Romeo then:
But look thou stay not till the watch be set,
For then thou canst not pass to Mantua;
Where thou shalt live, till we can find a time
To blaze your marriage, reconcile your friends,
Beg pardon of the prince, and call thee back
With twenty hundred thousand times more joy
Than thou went'st forth in lamentation.
His goals--to publicly announce Romeo and Juliet's marriage, to make sure all their friends are happy with them, to get a pardon from the Prince, and to bring Romeo home in a joyous celebration--are ridiculously lofty and he has absolutely no reason to believe he can accomplish any of these things. None whatsoever.
We never get a chance to see exactly what Friar Laurence might have done to make those things happen because Juliet is so quickly betrothed to Paris and the friar has to act much more quickly than he ever dreamed. He has to think fast, and of course he resorts to the thing he specializes in--medicines that both cure and kill.
It is a terrible plan on a practical level, as there are too many variables which are out of the friar's control. He cannot control what happens at Juliet's house before she takes the potion, or even be sure that the potion will work (which he is at least marginally worried about). Then he has to get word to Romeo, which of course does not happen. Everything after that is purely about timing and whether the friar will arrive in time to avert a disaster.
To his shame, Friar Laurence is not able to keep Romeo from killing himself, but he certainly could have kept Juliet alive if he had not been more concerned about his own life and reputation than about a young, desperate girl with a knife.
This all begins because the friar makes a hasty and imprudent decision early in the play. Some want to believe that he did all of these things out of some desire to help young love flourish; however, he impulsively agrees to marry the two young lovers, hoping that this will end the feud between the two families. Even at the ceremony he has misgivings, but he is caught up in the moment and disregards his instincts. He is not a wise counselor.
His impulsive acts and plans get them all into trouble and cost two young people their lives. His plans fail because he does not take the time to be more reasoned when he can and because he has completely unrealistic expectations of what he can accomplish. Though he may have been quite sincere in all of these things, his motives were questionable, at best. His plans failed because they were ill-conceived and dependent on too many factors which were out of his control.