I can't speak for your particular make but I had the same problem recently on my 307.

There was a service bulletin posted by Peugeot that said you had to overfill the power steering reservoir to above maximum - but not so it spills out.

I did this and supplemented it by taking off my wheel and wheel arch liner and cleaned and waterproofed the power steering electrical connector - on the 307 its in quite an exposed position.

I've also heard that an old battery can also cause this - the whine goes away after the car has been running a few minutes.

Like I say, they're Peugeot specific but its a couple of things to investigate that don't cost.