Starting problems. HELP!

Ok so it's been a while now since my car is doing this. Each time I start the car it seems to start very poorly (COLD starts only), as if its not going to start (not instant key turn) and when it does the rpm drops below 1000rpm and starts varying from 1200 to 900 rpm and all the lights start flickering till the car is warmed up (dimming at 900rpm then normal at 1200 and on and on)

And for the record my battery died in a year
I did my research and they are typical alternator problems
Renault said they diagnosed the car and its all good. i think they are saying that to charge me for a new alternator next year when my warranty's up...

Anyone had the same problem? This problem has benn an issue for 4 months
Thx