And while they are working - and the students learning - they are subject to no syllabus or exam board of any kind. There are no prescribed "units" for them to follow, no learning outcomes to be worked towards, and no detailed assessment criteria to ensure that every last dot and comma of said outcomes have been sewn up and nailed down to the satisfaction of some eagle-eyed verifier.
Essentially, the class has the freedom to study whatever they collectively decide to. And when that decision has been made, the teacher designs her programme of classes around their wishes.
Not only that, but the operations of the class are subject to no quality cycle; no one has to sit up inventing details for a self-assessment report or worrying over what to put in their quality improvement plan. No targets are set and met (or rather not met, as is more usually the case) here.
No third party can knock on the door, demanding admission and the opportunity to tyrannise the teacher with their tick-list of must-see teaching techniques. And, of course, it goes without saying that this is an Ofsted-free zone.
Now, you might ask, how can such outrageous things be happening in a sector that is so controlled and regulated that you can hardly break wind without someone making a note of it and storing it away for consideration?
The answer of course is that it isn't. It isn't happening in a college or any other premises licensed by the state. Where this unusual class is actually taking place is in my own back room. And it represents, in effect, the latest round in my ongoing battle with French.
I have tried it the other way - the college way - and it has never quite worked out. Somehow the classes on offer don't cater for what I want. Yes, I want to learn, but no one is interested in funding learning these days; it's assessment and qualifications that the cash comes tied to. And what exactly is a man of my venerable years supposed to do with an NVQ level 2 in crucifying the French language?
Thus I find myself in the curious position of being an advocate of public education, while at the same time setting up a new class in what is effectively the private sector. I have to say, though, that it wasn't difficult. My two friends, like me, spend some weeks every year in France. Like me, they speak French like a parrot speaks English - except perhaps with a smaller vocabulary and a worse accent than the parrot. Like me they want to improve. So we found a teacher, agreed on an hourly rate and away we went. Start up time: three days!
But could such a model actually be made to work in the public sector? Surprisingly, the answer to that question may be yes. At least there is evidence of it working in one particular case. As reported in the pages of FE Focus earlier this month, Lambeth College is working with the charity St Mungo's to help improve the basic skills of homeless people in London who are finding it difficult to get back into work.
Like my DIY French classes, this takes place where the students live - in their hostel - rather than in the college itself. Like my class, too, the participants design their own course, with college staff on hand to ensure that numeracy and literacy are integrated into whatever they do.
Such innovative work can only exist if some of the usual FE "must-haves" are put aside. For instance, no one can guarantee that the students will still be around at the end of their course given that they all live in a hostel for the homeless.
As Lambeth principal Richard Chambers points out: "If you were to judge the work we do in terms of FE performance indicators, it would never get done."