It's not really a matter of left & right, since some people are left handed so their dominant hand is different.
I'm right handed, so if I'm using a knife and fork as a pair, using the fork to hold the food and the knife to cut it, then I'll hold my fork in my left hand and my knife in my right (dominant) hand, as cutting or sawing requires more control than pinning.
However, if I'm using my fork mainly to shovel or skewer food that doesn't require cutting, then I'll hold it in my right (dominant) hand and usually put the knife down, or hold it in my left hand but only use it as an accessory to guide food onto my fork, not as a cutting tool.
Additionally, there is actually a "correct" way of eating, it's called Dining Etiquette (and varies from culture to culture). There's no law against not following it, but don't be surprised if you're called out for no eating "correctly" as the established norms of Etiquette dictate.