Ok, not a new car, but surely one that captures something of the essence of the Renault 4 (as well as the mini and 2CV) is the Nissan PAO, when they went all retro on us a while back. A sweet little car with not a computer controlled something to be seen anywhere near it. Basic motoring with some character. A rare car now as well.
I remember reading that the Nissan Pao was a tribute to a Renault 4 and I took it to be true.
But now when I look at it, I can't see any cues that are specific to the Renault 4.
It looks like a general mix of features: The profile is reminiscent of the 1st generation Honda Civic, the rear side window is 2CV-inspired and the front looks like the 1st generation, pre-facelift Toyota Starlet.
I don't think they had any one specific car in mind when they concocted it.