Can I fence with my left foot forward if I'm right-handed?

Not in Olympic fencing. Your front foot always matches your weapon hand: if you hold the weapon in your right hand, your right foot leads, pointing at your opponent, and your left foot sits behind, turned out to the side. Left foot forward with the weapon in your right hand puts your sword arm at the back of your body and your empty arm and shoulder closest to the opponent, which undoes almost everything the stance is built for.

Think about what the stance has to do. Your weapon arm needs to be in front so it can threaten, parry and riposte at full reach. Your body needs to stay sideways and narrow so there is less to hit. And the lunge drives off the back leg toward the front foot, which only works when your weapon arm reaches the same way. Leading with the wrong foot shortens your reach, hands the opponent a wide, flat target, makes parrying close to impossible, and leaves your unprotected arm as the first thing they meet.

The rules push back too. In foil and sabre, covering valid target with your non-weapon arm or by any abnormal position earns a yellow card, and any touch you score in that action is annulled. Using your free arm or hand to block or parry is a red card, which gives your opponent a touch. In épée the whole body is target, so the forward arm and shoulder simply get hit. You also may not switch the weapon to your other hand during a bout, unless the referee allows it after an injury to your hand or arm.

If left foot forward truly feels more natural, it may be a hint rather than a mistake: try holding the weapon in your left hand. Fencing left-handed with the left foot leading is completely legal and normal, and about one person in ten is left-handed anyway. Ask your coach to watch your footwork both ways for a few sessions and to check which leg you push off best. Boxing and batting both have right-handers lead with the left side, which is why the fencing stance can feel backward at first. Decide early, before habits set in, and remember a lefty needs a left-handed jacket, underarm protector and glove.