I want to sell my home to my grandson, can I draw up an agreement and have it notarized and file it with the state ? Would that be legal and put it in his name with me being the finance party ?

Yes, but generally such an agreement would be recorded not with the state but with the county clerk (or parrish in Louisiana). Invest a few hundred dollars to get a lawyer help you with this right; otherwise I guarantee you will make mistakes which will cost you or your grandson much more in the long run.

You might be able to save some money by getting a title company to handle the transfer. But I would not just D-I-Y it.