Here is your Applet. It had a great many problems. Now it draws a
horizontal red line.  I changed all the public classes to default so
that I could put everything in one file.

import java.applet.Applet;
import java.awt.Color;
import java.awt.Frame;
import java.awt.Graphics;
import java.awt.event.WindowAdapter;
import java.awt.event.WindowEvent;

public class Optique extends Applet

// all methods for doing this are missing.
// implements ActionListener,
// KeyListener, MouseListener, MouseMotionListener
  {
  Droite axe = new Droite( 80,420,0,1,0,0,800 );

  public void init()
     {
     // moved code to paint, no graphics object available here.
     // axe.traceSegment(this);

     }

  public void paint( Graphics g )
     {
     System.out.println ( axe );

     // must pick a colour, or you will just paint white on white
     g.setColor( Color.RED );

     axe.traceSegment(g);
     }

  /**
   * Allow this applet to run as as application as well for testing
   *
   * @param args not used
   */
  public static void main( String args[] )
     {
     final Optique applet = new Optique(  );
     final Frame frame = new Frame( "Optique" );
     frame.setSize( 1000, 1000 );
     applet.init();
     frame.add( applet );
     frame.validate();
     frame.setVisible( true );
     applet.start();
     frame.addWindowListener(
                            new WindowAdapter ()
                               {
                               /**
                                * handler on window close
                                *
                                * @param e      event details
                                */
                               public void windowClosing (
WindowEvent e )
                                  {
                                  applet.stop();
                                  applet.destroy();
                                  System.exit( 0 );
                                  } // end WindowClosing
                               } // end anonymous class
                            );
     } // end main

  }

/**
* Point renamed to PointXYZ avoid confusion with java.awt.Point
* Defines a point in 3D cartesian space
*/
class PointXYZ
  {
  double x;
  double y;
  double z;

  PointXYZ()
     {
     this.x=0;
     this.y=0;
     this.z=0;
     }

  PointXYZ(double x, double y,double z)
     {
     this.x=x;
     this.y=y;
     this.z=z;
     }

  public double getx()
     {
     return this.x;
     }

  public double gety()
     {
     return this.y;
     }

  public double getz()
     {
     return this.z;
     }

  public void set(double x, double y,double z)
     {
     this.x=x;
     this.y=y;
     this.z=z;
     }

  public void setx(double x)
     {
     this.x=x;
     }

  public void sety(double y)
     {
     this.y=y;
     }

  public void setz(double z)
     {
     this.z=z;
     }
  }

/**
* defines a direction with x,y,z
* Instead of duplicating code, we inherit it from PointXYZ
*/
class Direction extends PointXYZ //cosinus directeurs
  {
  Direction()
     {
     super( 1, 0, 0 );
     } // x direction principale, axe optique

  Direction( double x, double y,double z )
     {
     super( x, y, z );
     }

  }

/**
* defines a 3D line segment
*/
class Droite
// I don't think you mean extends Graphics.
// This class has nothing to do with the java.awt.Graphics class.
// extends Graphics
  {
  double x1, y1, z1, x2, y2, z2;

  Droite()
     {
     this.x1=0;this.y1=0;this.z1=0;
     this.x2=0;this.y2=0;this.z2=0;
     } //point (0,0,0)

  Droite(PointXYZ p,Direction d,double dist)
     {
     this.x1=p.getx();
     this.y1=p.gety();
     this.z1=p.getz();
     double dx=d.getx();
     double dy=d.gety();
     double dz=d.getz();
     this.x2=x1+dist*dx;
     this.y2=y1+dist*dy;
     this.z2=z1+dist*dz;
     }

  Droite(double x1, double y1, double z1,
         double l, double m, double n, double dist)
     {
     // is no p.
     //this.x1=p.getx();
     //this.y1=p.gety();
     //this.z1=p.getz();
     // I presume you mean
     this.x1=x1;
     this.y1=y1;
     this.z1=z1;

     this.x2=x1+dist*l;
     this.y2=y1+dist*m;
     this.z2=z1+dist*n;
     }

  Droite( PointXYZ p1, PointXYZ p2 )
     {
     this.x1=p1.getx();
     this.y1=p1.gety();
     this.z1=p1.getz();
     this.x2=p2.getx();
     this.y2=p2.gety();
     this.z2=p2.getz();
     }

  public void traceSegment(Graphics g)
     {
     // drawLine takes int values
     g.drawLine((int)this.x1,
                (int)this.y1,
                (int)this.x2,
                (int)this.y2);//tracé en 2D
     }

  /**
   * debugging tool
   *
   * @return string representation of the line
   */
  public String toString()
     {
     return
     "x1:" + x1 + " y1:" + y1 +  z1:" + z1
     + " x2:" + x2 + " y2:" + y2 + " z2:" + z2;
     }

  }