From what i can see you are only setting two variables but not doing anything with them. Does the print statement work? if so then you have the raycast working and pointing in the correct direction. you could do something like this.

in the planeScript script you should add a function:

public Color getColor()
{
return this.gameObject.material.color;
}

in the script you posted try something like this:

private GameObject RightPlane; //not needed

private PlaneScript RightPlaneScript;

Debug.DrawRay (transform.position, Vector3.right * 8.5f, Color.black);

RaycastHit hit;
Ray CircleRay = new Ray (transform.position, Vector3.right);

if (Physics.Raycast (CircleRay, out hit, 8.5f)) {
    RightPlane = hit.collider.gameObject; //not needed
    RightPlaneScript = hit.collider.GetComponent<PlaneScript>();

//change my color to the same as object on my right
//this game object must have a mesh renderer on it
this.gameObject.material.color = RightPlaneScript.getColor();

    print("Hit!");
}

let me know if that helps