This answer describes a solution for a soft sci-fi scenario which is internally consistent but not necessarily founded on hard science.
More jumping, less standing around
One reason why real-life fencing is rather static, is because defense is more important than offense and the most reliable way to defend is not to dodge but to parade the attack with your weapon. That means fighters keep their weapon close to their bodies to parade any enemy attacks.
To favor a more offensive and mobile fighting style, have energy-based melee weapons which can not block each other. That means the only way to prevent getting hit is dodging. Your fighters will jump and roll around a lot during combat, making for some very spectacular acrobatics.
The only reason why you would use a spectacular wide swing instead of a short poke is because it gives you much more speed and thus more impact energy. This could matter when your target got some kind of protection which negates any impacts which are not fast enough. The only way to build up enough momentum to break through is to use wider swings.
Armor would be counter-productive, because it would make the fighters less mobile. But what about a personal force field which covers the whole body and only lets the aforementioned energy weapons pass through when they move very fast?
This force-field technology could also be used to justify why nobody brings a gun to an energy-sword fight: Have the force-fields block any personal firearms but not personal melee energy weapons.
Going beyond human capabilities
The major factor which holds your fighters down is their human clumsiness. Only a few extraordinary humans possess the agility, dexterity, strength and spacial awareness to perform all these movie-like stunts, and even those only when choreographed carefully. To see such action pulled off in life-or-death combat by your relatable everyman protagonist, you need to augment them somehow. You could, for example, give your futuristic high-tech fighters exoskeletons or artificial limbs which enhance their speed and jumping capabilities and neuro-implants or drugs which enhance their reaction speed and spatial awareness.