Trouble carrying over scripted gravity to NPC.

I'm having trouble getting my NPC to get on the ground. It uses the same asset as the player, the asset doesn't have any inherent components. Here is just enough of my player movement script to give an idea of how I keep it on the ground without a rigidbody.

 public class FoxMovement : MonoBehaviour {
 
 
     public float gravity = 5.0F;
 
     private Vector3 moveDirection = Vector3.zero;
     void Start () 
     {
     }
 
     void Update() {
         float movespeed = Input.GetAxis ("Vertical");
 
         CharacterController controller = GetComponent<CharacterController>();
 
         if (Input.GetKey (KeyCode.A))
             transform.Rotate (Vector3.up * Time.deltaTime * -rotationSpeed);
         if (Input.GetKey (KeyCode.D))
             transform.Rotate (Vector3.up * Time.deltaTime * rotationSpeed);
         if (controller.isGrounded) {
             moveDirection = new Vector3 (0, 0, Input.GetAxis ("Vertical"));
             moveDirection = transform.TransformDirection (moveDirection);
             moveDirection *= speed;
 
 }
         moveDirection.y -= gravity * Time.deltaTime;
         controller.Move(moveDirection * Time.deltaTime);
 
         }
 
 
 }

Here is the current enemy-controlling script.

 public class BasicEnemy : MonoBehaviour
 {
     public Transform target;
     public float speed = 3f;
     public float attack1Range = 1f;
     public int attack1Damage = 1;
     public float timeBetweenAttacks;
     public Transform myTransform; //current transform data of this enemy
     public int rotationSpeed = 3; //speed of turning
 
 
 
     // Use this for initialization
     void Start ()
     {
         Rest ();
         myTransform = transform;
     }
 
     // Update is called once per frame
     void Update ()
     {
     }
     }
 
     public void MoveToPlayer ()
     {
         Debug.Log ("Moving to player.");
         //rotate to look at the player
         myTransform.rotation = Quaternion.Slerp(myTransform.rotation,
             Quaternion.LookRotation(target.position - myTransform.position), rotationSpeed*Time.deltaTime);
 
 
         //move towards the player
         myTransform.position += myTransform.forward * speed * Time.deltaTime;
     }
 
     public void Rest ()
     {
     }
 }

I've tried transferring the gravity references to the way the NPC moves but it's dependent on vector3 and input which the NPC doesn't have. What is the smart thing to do here? Educate me please.

Sticking a rigidbody with gravity on it makes it fall through the world, despite multiple collider configurations.