How do I defend against an opponent with a really fast attack?

Do not try to out-react a fast attack once it has started; take away what it needs. A fast attacker needs a clean run-up: room to accelerate and a distance they can read. Your job is to deny that with distance and timing, so they either finish from too far and fall short, or have to slow down to deal with your blade. Retreating faster helps, but reacting late to an attack that is already flying will lose most of the time, however good your parries are.

Control the distance. Do not sit at exactly the spot they like to launch from. Mix it up: take one big step back to make them chase, then stop short so their final lunge comes from too far; sometimes step forward a little to cramp their run. Change the pace of your retreat so they cannot time the finish. Parry late, when they commit to the final action, not at their first step, and pick one or two parries you trust (four and six in foil, six, four and eight in épée, tierce, quarte and quinte in sabre) and drill them while moving backward.

In foil and sabre, a correctly executed attack has priority, so a counterattack into a simple fast attack loses even if both lights go on. A counter only wins against a bent-arm march, which is preparation, or when it lands a full tempo before the final movement of an attack with feints. Point in line set before they start forces them to deflect your blade first, and contact alone is not enough; if they run onto it, the touch is yours, but if they beat it aside you must parry. In sabre the hit must arrive by the time the front foot lands, and the flèche and crossover steps are banned, so pulling distance to make the finish fall short is a core skill. When it misses, go immediately.

In épée there is no right of way, so you can simply hit first: a stop hit to the wrist or forearm as they come in, ideally with opposition or with a step back so their attack falls short and yours lands. If you are ahead, a double is fine. For practice, have a partner march and lunge at random moments while you work on breaking distance and parrying on the last step, and do ladder footwork with sudden changes of direction. Video of your bouts shows exactly where their acceleration starts.