That is a long drive, about 10 hours without any stop, and I would not attempt it in a single day. You can take the autoroute the entire way and make Amboise in almost 7 hours with no stops. Autoroute costs alone will exceed 110€. If you stop much along the way, it will be 2 full days of driving.
I would not take A7 towards Lyon. There is not much of anything to see near the autoroute unless you want to make it 3 days.
That leaves A75 farther to the west which has a number of wonderful points of interest up to Clermont Ferrand. Between Clermont Ferrand and Amboise, it is not really a compelling area. I would probably just rejoin the autoroute, A71, near Clermont Ferrand and stay on it until Amboise.
Back to points before Clermont Ferrand, from Avignon you can choose either the road via Le Puy-en-Velay which is a wonderful city and should not really be missed. Or you can head to A75 passing just south of Mende. A75 is a toll free autoroute. The only charge is 5€ when passing over the Viaduc de Millau which will be south of your position. To cross the viaduc you would need to travel A9 towards Montpellier and pickup A75 from Monpellier. It would add time but the viaduc is one of the current engineering marvels of the world.
I would take A75 but divert west to pickup Saint Chély d´Aubrac or specifically Aubrac itself just to have lunch at Chez Germaine. You could also head to Laquiole to purchase some of their famous knives. If you were to do this, buy knives from Calmels, the original Laquiole knife producer. I would proceed north to St Flour and rejoin A75 northbound.
Another amazing point of interest along A75 is the Viaduc de Garabit just south of St Flour. This bridge was constructed by Gustav Eiffel, it really looks like a horizontal Eiffel Tower. It is illuminated at night projecting itself over the lake in a very majestic manner. I often stay at the Beau Site Hotel. The views from the dining room at night of the illumined bridge are amazing.
There is a lot to see and to visit between Avignon and Clermont Ferrand and, in my opinion, not much thereafter.