What happens is the attack gets stronger
Devil fruit eaters legit become 1 with their fruit
Haki isn't a swordsman exclusive ability or power up like some of yall try make it
Yes, the users become one with their DF, but Haki isn't required for that. With swordsmanship however, Haki is said to be the link connecting the swordsman to the sword.
Of course, not all fighting styles benefit from Haki equally. Punching (Luffy, Garp) of course also benefit more from it than elements. Garp hitting you with hardening, internal destruction and CoC infusion would be quite different from trying to infuse said Hakis with fire.