You car could indeed be damaged in some way, but I would suspect the effect of that would be to get worse with speed not better.
There are a number of generic issues you could be experiencing.
Firstly, as has been said, the car is sat on the bump stops negating most of the suspension movement. However this said should not smooth out as speed increases and and significant undulation on the road is going to have you commenting that the car is trying to send you backwards into the ditch rather than a wobble. It also should be very apparent to anyone looking at the suspension on a 4 post lift.
Then you get into the technical stuff. Lowering springs are, if they have been thought about, will be shorter to lower the car. However because this now reduces the total amount or remaining compression (before you reach the bump stops) they are going to be stiffer to resist all the loads before the bump stops. Looking at my standard car there is about a 3" gap between the rear tyre and the top of the arch. Feeling underneath the arch there is about 2" to the arch liner. so using some total man maths assume there is 5" of total suspension compression on the rear. Again assume that to fully compress that needs a 500kg load. That gives us 100kg per inch of compression, nothing like mixing units! Now, if you want to reduce that arch gap to 1" you reduce the total compression travel to 3" or a 40% reduction in travel. However in spring rate terms, using the same 500kg load to get to full compression you now have 500/3 = 166kg per inch or 66% stiffer spring. So what this means is you will naturally bounce a lot more on bumps, particularly of the light rear end.
Taking this further however you get into the damping. If you are still using the standard dampers you are now asking them to do 66% more damping in 40% shorter distance, most particularly in droop when the damper is trying to control the extending spring. Long and short of this the damper is overworked and the suspension is under damped.
This shows up particularly on the high frequency, low amplitude bumps such as broken road surfaces, road joints and the like that will cause the wheels to jiggle and the body to wobble. I have driven cars with "coilies" that quite literally feel like cut and shut cars with the front and read reacting in a totally different way to each other. As speed increases these road imperfections become somewhat less obvious as the car tends to skip over them more and also the tyre compression will take a bit out and the road undulations become more apparent which bigger, higher amplitude bumps, are lower frequency and suspension copes far better. Remember, Renault and it's suspension partners will have spent a lot of time (money and effort) tuning dampers to springs. If they had planned the car to be lower, the OEM damper settings would have been different.
Long answer, but I have seen lots of times where stiffer springs without correspondingly up-rated dampers result in a sh1t ride.
Finally, however, have you actually checked tyre pressures? It never fails to amaze me the number of "help, my car does not drive right" threads that get started, have people say they have looked at every single mechanical issue, only for the OP to come back 8 weeks, yes literally, and say that it is all alright now because they eventually they checked the tyre pressures and one tyre was at 8psi and the other at 32!