My character moves according to global Vectors

This seems like it should be something simple, i'm moving my character by changing his velocity with a camera locked behind my player, which i can rotate it around and snap it back behind him whenever he change his direction.

The problem is when i move my player, for exemple, to the right and snap the camera behind him to look at his forward vector then try to move forward, my character will move toward the global forward Vector (in this exemple you'll see your character going to the left)

Anyone have any ideas?

Here's My HeroControll Script:

 using UnityEngine;
 using System.Collections;
 
 [RequireComponent(typeof(Rigidbody))]
 [RequireComponent(typeof(Animator))]
 [RequireComponent(typeof(CapsuleCollider))]
 
 public class HeroControll : MonoBehaviour {
 
     public float PlayerSpeed,jumpHeight;
     public bool grounded,moving;
     public GameObject Camera;
 
     private Rigidbody rg;
     private Animator anim;
     private float forwardInput, turnInput;
     private bool runInput;
     private int r;
     private RaycastHit hit;
     
 
 
     // Use this for initialization
     void Start () {
         rg = GetComponent<Rigidbody>();
         anim = GetComponent<Animator>();
         forwardInput = turnInput = 0;
         jumpHeight = 10f;
         PlayerSpeed = 10f;
         grounded = true;
         moving = false;
     }
     
     // Update is called once per frame
     void FixedUpdate () {
 
         //Get Inputs
         forwardInput = Input.GetAxis("Vertical");
         turnInput = Input.GetAxis("Horizontal");
         runInput = Input.GetKey(KeyCode.LeftShift);
       
 
         //Set Animations
         if ((turnInput != 0) || (forwardInput != 0))
         {
             moving = true;
             anim.SetBool("walking", true);
         }
         else
         {
             moving = false;
             anim.SetBool("walking", false);
         }
 
         //Update velocity 
         rg.velocity = new Vector3(PlayerSpeed * turnInput, rg.velocity.y, PlayerSpeed * forwardInput);
 
         //Set Directions
 
         moveDirection = new Vector3(turnInput, 0, forwardInput);
         if (moveDirection != Vector3.zero)
         {
             Quaternion newRotation = Quaternion.LookRotation(moveDirection);
             transform.rotation = Quaternion.Slerp(transform.rotation, newRotation, Time.deltaTime * 8);
             
         }
     }
 }

and My CameraControll Script :

 using UnityEngine;
 using System.Collections;
 
 public class CameraZelda : MonoBehaviour {
 
     private GameObject player;
     private float smooth,orb;
     public Transform target;
 
     private Vector3 offset;
 
 
     // Use this for initialization
     void Start () {
         player = GameObject.FindGameObjectWithTag("Player");
         smooth = 30f;
         offset = player.transform.position - transform.position;
     }
     
     // Update is called once per frame
     void Update () {
         transform.position = player.transform.position - offset;
         
 
         orb = Input.GetAxis("orb");
         transform.RotateAround(player.transform.localPosition, Vector3.up, smooth * orb * Time.deltaTime);
 
         changeTarget();
         
         
     }
 
     void changeTarget()
     {
         if (Input.GetKey(KeyCode.C))
         {   
             transform.position = Vector3.Slerp(transform.position, target.position, smooth * Time.deltaTime);
             offset = player.transform.position - transform.position;
             Quaternion rotation = Quaternion.LookRotation(player.transform.forward);
             transform.rotation = rotation;
             transform.eulerAngles = new Vector3(20f, transform.eulerAngles.y, transform.eulerAngles.z);
 
         }
     }
 }