Unless you are already used to staying up all night and concentrating (eg shift worker rather than party-goer) I'd say don't underestimate the effect of a shortage of sleep. Normally, if this was just a matter of picking your own start time, I'd suggest starting just before first light 4am ish. That way you could go to bed early, get a good kip and you would then only be staying up for the first part of the second night. In other words, it would be as near as possible to a normal sleep pattern, but with an early night followed by a late one. In some ways, midnight to midnight might be better, but on the basis that you can probably cover the greatest mileage when you are still fresh, no point in wasting that fresheness riding more slowly in the dark at the start of the ride.
Having said all that, if you have a choice of ferry time, I'd consider working around that to get in a bit of kip because even twenty or thirty winks instead of the full forty can be a great refresher.
Apart from that, it's what I always post about distance cycling - coping with what goes on in your head is at least as important asyour legs. A shortage of sleep can make the bonce even more dodgy. Get as much mileage in as you can, preferably together, with plenty of night riding. A well-motivated group riding together should eat something like this, but one whinger or show off could be very disruptive. A group can also waste a lot of time if everybody wants to mess about individually with stops etc. It's staing the obvious but any number of riders taking a five minute break together loses five minutes. Four riders each calling their own 5 minute time out is 20 golden minutes gone forever. It's much easier to lose time than to make it up so this needs firm discipline.
I think the distance should be do-able by a group of reasonably fit riders. One small tip which I know from experience - try to avoid paying too much attention to French road signs with distances measured in kilometres. Not very easy when they are at every turn. I have found that immediately converting all distances into miles helps. "Only sixty miles to go" is a lot more encouragingt than, "Oh heck - it's still another 100K."
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PS I suppose a lot also depends on your reception at the destination. If you are going to visit friends / family etc., it should be no problem but if not, it's something needing some thought. I once arrived in Avignon in the small hours and much earlier than expected with nowhere to go but a bench. It was bad enough arriving by train, rather than by bike, but after a very long journey, it's something to avoid.
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PPS Although some of my longest cycle rides as an idiotic teenager were spur-of-the-moment affairs, I think a bit of planning is likely to improve the chances of success and an enjoyable ride.
I think you need to think about how you will deal with contingencies, including "showstoppers" (in the current lingo.) If somebody becomes ill or gets a serious mechanical, will everybody stop, one person stop while the others continue or what? Although any decision would have to depend on circumstances, agreement in advance may stop hours being lost having a discussion from first principles. Obviously, a lot depends on priorities. eg is a good ride more important than doing it in under 24 hours?
I think then it's important to know from experience what you can expect as your group's cruising speed. By this I mean how fast the group can travel for hours on end without expending too much energy but making decent speed. For ease of calculating, I'll take 15mph. That would mean just short of 19 hours riding time for 280 miles. If you are allowing 24 hours start to finish, your three hours crossing the Channel leaves 21 hours. So, with a cruising speed of 15 mph you have a margin of two hours for stops. Now, if you allow 5 mins stoppage per hour, that's just over an our and a half. That leaves "only" 30 mins for a longer stop. Of course, there's no reason to stop for 5 mins every hour, but working it out like this gives a better idea of what's involved than dividing distance by time and saying that's the average. Knowing your realistic cruising speed also helps if you have to alter your plans and you are planning a realistic
étape. (Calculations are e&oe, of course

)
As with all long rides, don't make the mistake of starting too fast when the adrenaline of starting the big event would allow racing speeds. Save some energy for the last 50 or so miles.