She’s definitely force sensitive. The original movies stated as much and it was demonstrated in the new movie. She was on a different planet when Han died but we saw her feel his death. It seems that she just pursued a political/leadership path rather than a traditional warrior’s path. Plus, if the only people in the galaxy with any training in the force are either evil or your twin brother, you may be disinclined to have them train you.

She totally should be a Jedi, though.