Perspective issue with railgun/raycasting

I would like to create a Railgun in the style of Quake. Here is what i achieve so far :

That's okay but this is because I target the void. When I target an object closer to the player, here the ground for instance, the beam isn't on the crosshair :

An other exemple :

So the raycast and the line renderer are starting from the guntip of my railgun and i think this is a problem of perspective (because the gun isn't align with the camera).

Here is the script i use (I took this script from the survival shooter tutorial project, and tweaked it a little bit):

 using UnityEngine;
 
 public class RailgunShot : MonoBehaviour
 {
     public int damagePerShot = 1;
     public float timeBetweenBullets = 1f;
     public float range = 100f;
 
     float timer;
     Ray shootRay;
     RaycastHit shootHit;
     LineRenderer gunLine;
     float effectsDisplayTime = 0.1f;
 
 
     void Awake()
     {
         gunLine = GetComponent<LineRenderer>();
     }
 
 
     void Update()
     {
         timer += Time.deltaTime;
 
         if (Input.GetButton("Fire1") && timer >= timeBetweenBullets && Time.timeScale != 0)
         {
             Shoot();
         }
 
         if (timer >= effectsDisplayTime)
         {
             gunLine.enabled = false;        //Disable effect.
         }
     }
 
     void Shoot()
     {
         timer = 0f;
 
         gunLine.enabled = true;
         gunLine.SetPosition(0, transform.position);
 
         shootRay.origin = transform.position;
         shootRay.direction = transform.forward;
 
         if (Physics.Raycast(shootRay, out shootHit, range))
         {
             gunLine.SetPosition(1, shootHit.point);
         }
         // If the raycast didn't hit anything...
         else
         {
             gunLine.SetPosition(1, shootRay.origin + shootRay.direction * range);
         }
     }
 }
 

Can you help me solve this ? Thanks in advance.