I don't think it's a great idea, especially since you will be in Beaune for such a short time. But I won't say it's a mistake, since it's not impossible and is pursuit of something you obviously want to do.
The case against it goes like this. Your drive to Versailles will likely be in heavy traffic, and then you'll need to deal with parking etc. You can spend as much or as little time there as you like, but many people spend most of a day.
Then too, the drive to Beaune is not short. And you will probably be at least a little jet-lagged, making everything less fun and more work. It's just a whole lot of logistics on that first day, after a long jet ride.
There's not a whole lot that is like Versailles, but there are some wonderful sightes enroute to Beaune, such as Vezeley or the Fonteney Abbey. The La Rochepot castle, just south of Beaune, is worth a visit too. And Beaune is really nice.
Have a great time!