From Paris, it's possible to fly to Dundee, changing at LCY. Trouble is: from a Paris airport to Dun

You do not seem to have done very much research yourself. The airport you request is Edinburgh and to get to St. Andrews, you can rent a car at the airport,or go into Edinburgh and take the train or bus. Don't expect to get to play golf on the Old Course unless you have made a booking months ago.
A little bit harsh almcd. The only practical option is to fly to EDI from Paris on Air France or EasyJet. Ideally pick up a hire car at EDI and drive up to StA (approx 1 hour), or longer if you want to take the scenic route via the Fife coast.
If you really don't want to drive yourself there are several airport car services operating out of StA that will collect you (an expensive option though). Otherwise, get yourself by bus/laxi to Edinburgh Haymarket station and take the train the Leuchars, followed vans warped tour by local bus/taxi into St Andrews.
From Paris, it's possible to fly to Dundee, changing at LCY. Trouble is: from a Paris airport to Dundee airport takes about three times as long as flying to Edinburgh. And costs about three times as much.
So, if the weather is suitable, my suggestion - a bracing walk out along West Sands as far as Eden Point to see the seals and then turn and enjoy the best views of St.As ahead of you on your return, so far as The Himalayas. Then a short (40min) diversion amongst the hillocks and tussocks before heading off to the bar of the Russacks Marine vans warped tour (just over the Swilkin Burn) half away along the 1st/18th joint fairway for a glass or two of something warming.