That's a tricky one to answer! The short answer would probably be yes, but it's the compromises you'd have to make that might make you rethink. For instance, you'd have to go through France first, and then all of the other countries you've listed, which gives a total of 9 countries (excluding the U.K.) in 28 days, so roughly three days per country, which for me, isn't a lot of time, although some of those you would just zip through quickly to get to the next one (e.g. France in the beginning, as you say you'll visit it later), so that will give you more time in some of the other countries.
If I were you I would use some route planning software (e.g. Tyre) to put a basic route together. It will then tell you how much drive time you have, and then you can factor in how much you're willing to drive per day, and then where and for how long you want to stop in places. You'll soon see if you've got it about right or not. This is how we plan all of the countries we visit, as we are on a timescale to get to Mongolia at the right time weather-wise this summer (one year into an around the world trip). Try and add a little contingency though, as there will be times when you're too knackered to move on!
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