Barron is smart enough to leave her $1.00 and nullify any challenge to his will. That happened to several of my relatives who pissed off my Great Grandfather. The old man doesn’t own the company anymore but somehow I think he’s still calling the shots with the family and remember we’re talking about a whole lot more than just a few million.
That's not the way it works.In every state (except,I believe,Louisiana)if a person is related to a deceased person in certain ways (child,spouse,sibling,etc) *or* if they've been given something of value in a previous will written by the deceased that person has "standing" to challenge a will in a probate court.
Challenges can be based on illness (mental or otherwise),undue influence and other things.
Assuming that Paris was ever a beneficiary of a will written by her grandfather she can challenge any subsequent one.And one might assume that the basis of her challenge would be illness ("my grandpa wasn't in his right mind when he wrote the will(s) that disinherited me") or undue influence ("my uncle/cousin,etc lied to my grandfather and conspired against me in order to enrich himself").
A challenge by her wouldn't necessarily be successful if decided by a judge or a jury but oftentimes the executor might settle out of court with a challenger in order to save time and money (will challenges are usually very expensive and very lengthy).So she might be thrown a few million by the executor in order to make her go away.