To start with, Charles VI, mad or not would probably not be in the position to order an assassination at the age of 8 while his father still reigned. In 1376, that order would have to come from his father, Charles V, who was a far less volatile personality. If he disapproved of the actions of the Pope, his methods would probably imitate Philip the Fair; a trusted adviser would be sent south to "convince" the Pope of the error in his ways. Through threats, or perhaps force, the Pope would change his tune, and if he died during or after the persuasion, well such things happened in the Middle Ages.
All an assassination, or suspicious death of the Pope would accomplish in this case would be to continue the Avignon Papacy, and possibly move up the date of the Western Schism. If the former, another Frenchman would be elected Pope due to the influence, and perhaps the coercion of the French Crown. The grumbling within the Church outside of France would get louder. All that it would take would be the spark of some sharp division over a Pope, or a theological position to create a schism.
Even if the sole legitimate Pope continues to reign in Avignon for another generation, the French Crown (or the House of Valois) would have difficulty continuing to dominate the Papacy. Once Charles VI does comes of age, his incapacity would probably extend to ecclesiastical affairs. Even if his minsters managed to keep the Church under France's thumb and united, the Treaty of Troyes would probably transfer the effective custody of the Pope to the English.
Long term, the longer the Papacy remains under the sway of a secular ruler, the more its secular power is likely to decline. Even the nominal authority over Rome would probably be lost to the local nobles, or one of the Italian states, making the Pope in Avignon's claim to be the successor of St. Peter difficult to make.