I had the exact same problem with my 98 Coupe just after I bought it in November.
My remote was getting tempramental and so I thought the solution would be to change the batteries - wrong!.
I did this and the red light was still flashing on my remote but would not open the car or disarm the immobiliser.
At this stage I was not aware of the 'mobile phone' test so was unable to try this.
Basically, what i did was got a lift up to my local Renault dealer to get the emergency immobiliser over-ride code which was free but I have heard some garages may charge a small fee(you need proof of ownership and form of ID).
This lets your car start once (beware not to use this code frequently as it can damage your cars electronic management system and cost of repair is probably more than the car value I was told).
I then drove the car to the dealer and they diagnosed that the key was now faulty and I needed a new fob (as i predicted they would say).
I was told it could take up to 10 days for my new key to arrive but in fact I was pleased when they rang me after 3 days.
This was at the cost of £70 plus then they have to programme it to your car at cost of £30. Total bill £100 +vat.
The guy i spoke to was dead on and knocked the vat off so just charged me the £100.
Sorry if this is not what you wanted to hear but i seems to be a common fault.
It is possible they may just be able to re-programme your existing key which should be £30 +vat, but knowing a main dealer - i doubt it!
All the best,