This restaurant seems to have been here for ever - at least 25 years to my knowledge and probably longer. It is authentically French in many ways, although to me it's more like somewhere that you'd find in a Paris suburb than the country restaurant that they try to portray it as. The food is pretty reliable, which it should be because the menu doesn't change much, so they've had plenty of time to get it right. The quiche Lorraine is as good as you'll get anywhere in France - moist and rich, quite lovely. Other safe bets include the onion soup and the coq au vin. Some call it romantic, presumably because of the dim lighting and candles, though to my mind the table spacing means that any intimacies will tend to be communal.
The house wine, which is perfectly good, comes in one-and-a-half litre bottles (even if you order it as an aperitif), but the system is that you only get charged for what you drink.
La Poule Au Pot is said to be one of the most romantic restaurants in London, something which depends on the individual, but it is certainly one of the most authentically French. The cuisine is very rustic and wine is served in enormous carafe bottles - you pay for the amount you manage to consume rather than the entire bottle.