Not really enough info here to provide a good answer…
I just created a curve path, parented the default cube to it, choosing the follow path option, and got the defualt cube following my path. I then baked the animation, choosing the ‘visual keying’ option, then deleted the path object. Now the default cube moves as it did when it was a child of the path because it is key framed. Simple and it works.
If this doesn’t work for you, you might want to provide more information. What type of object is following the path? Is it a simple object, like a baseball, or a more complex object like a rigged character/machine? How are you doing the path animation? Via parenting or follow path constraint? What is the end result? I get it that you are exporting fbx, but exporting to where? A game engine?