Three Colors: Red

The film begins with clips that track a telephone call between London and Geneva, where a university student and part-time model, Valentine Dussault (IrÃ¨ne Jacob), is talking to her emotionally infantile and possessive boyfriend. During her work as a model she poses for a chewing-gum campaign and during the photo shoot the photographer asks her to look very sad. While walking back home, Auguste, a neighbour of Valentine's, drops a set of books, notices that a particular chapter of the Criminal Code opened at random, and concentrates on that passage. As she drives back to her apartment, Valentine is distracted while adjusting the radio and accidentally hits a dog. She tracks down the owner, a reclusive retired judge, Joseph Kern (Jean-Louis Trintignant). He seems unconcerned by the accident or the injuries sustained by Rita, his dog. Valentine takes Rita to a veterinarian, where she learns that Rita is pregnant. Valentine takes the dog home. Later, money is delivered to her apartment from an unnamed sender.
Whilst Valentine is walking Rita the next day the dog runs away and Valentine eventually finds her back at Kern's house. She asks and he confirms that the money sent to her came from him, for the vet bill. He then tells Valentine she can have the dog. A short time later Valentine finds Kern eavesdropping on his neighbours' private telephone conversations. The judge challenges Valentine to go tell the neighbours and initially she goes to do so. She visits the neighbours' house, which appears, on the surface, to contain a contented nuclear family, causing her to change her mind about exposing their secrets. She returns to Kern's house and Kern tells her that it would make no difference if she denounced him for his spying because the people's lives he listens to would eventually turn into hell anyway. She leaves saying that she feels nothing but pity for him.
Whilst visiting Kern, Valentine hears a phone conversation between her (unbeknownst to her) neighbour, Auguste, and his girlfriend, Karin (Frederique Feder). They discuss if they should go bowling. Valentine covers her ears but from the very little she hears she concludes that they love each other. Kern disagrees. That evening Valentine is alone at home and hopes that her boyfriend will call, but it is the photographer who calls, saying that her billboard was set up that evening and asks her to join them bowling to celebrate. Later, Auguste takes his exam and passes it and becomes a judge. Karin asks if he was asked any questions regarding the article that was open when he dropped his books. Auguste says yes. Karin gives him a fancy fountain pen as a gift and he wonders what the first judgment he signs with it will be. That evening, Kern writes a series of letters to his neighbours and the court confessing his activities, and the community files a class action. Later, at the law courts, he sees Karin make the acquaintance of and begin to flirt with another man. Earlier, Auguste had missed a call from Karin and tried to call her back but got no answer.
Valentine reads the news about a retired judge who spied on his neighbours and rushes to Kern's house to tell him that she did not report on him. He confesses that he turned himself in, just to see what she would do. He asks her in and shows her that Rita has had seven puppies. He tells her that in their last conversation when she spoke about pity he later realized that she really meant disgust. He ponders about the reasons why people obey laws and concludes that often it is more on selfish grounds and from fear than about obeying the law or being decent. It is his birthday and he offers her pear brandy for a toast. During their conversation he reminisces about a sailor he acquitted a long time ago, only later realizing he had made a mistake, and that the man was guilty. However, the man later married, had children and grandchildren and lives peacefully and happy. Valentine says that he did what he had to do, but Kern wonders how many other people that he acquitted or condemned might have seen a different life had he decided otherwise. Valentine tells Kern about her intended trip to England for a modeling job and to visit her boyfriend. Kern suggests that she take the ferry.
Auguste has been unable to reach Karin since graduation so he goes to her place and sees her having sex with another man. Distraught, he leaves. Later, Auguste sees Karin and her new boyfriend in a restaurant. He gets her attention by tapping on the restaurant window with the pen she gave him. But when she rushes outside, he hides from her. In a temper, he ties his dog by a quayside and abandons him.
Karin runs a service providing personalised weather information to travelers by telephone. Kern calls and enquires about the weather in the English Channel for the time when Valentine will be traveling to England. Karin states that she expects the weather to be perfect and reveals that she is about to take a trip there (with her new boyfriend who owns a yacht).
The day before Valentine leaves, she invites Kern to a fashion show where she is modeling. After the show they speak about the dream Kern had about her, where he saw her at the age of 50 and happy with an unidentified man. The conversation then turns to Kern and the reasons why he disliked Karin. Kern reveals that before becoming a judge, he was in love with a woman very much like Karin, who betrayed him for another man. While preparing for his exam, he once went to the same theatre where the fashion show took place and he accidentally dropped one of his books. When he picked it up, Kern studied the chapter where the book accidentally opened, which turned out to be the crucial question at his examination. After his girlfriend left him, he followed her across the English Channel but never saw her again, because she died in an accident. Later, he was assigned to judge a case where the defendant was the same man who took his girlfriend from him. Despite this connection, Kern did not recuse himself from the case and found the man guilty. He tells Valentine the judgment was entirely legal but also that he subsequently requested early retirement.
Valentine boards the ferry to England. Auguste is also on the ferry, clutching the dog he had temporarily abandoned. Although living in the same neighborhood and nearly crossing paths many times, the two have still never met. Suddenly a storm rises and sinks both the ferry and the boat with Karin and her boyfriend. Only seven survivors are pulled from the ferry: the main characters from the first two films of the trilogy, Julie and Olivier from Blue, Karol and Dominique from White, and Valentine and Auguste, who meet for the first time, as well as an English bartender named Stephen Killian. As in the previous films, the film's final sequence shows a character crying - in this case, the judge - but the final image replicates the iconic chewing-gum poster of Valentine, but this time with real emotion showing on her face.

Question: Across which body of water did Kern follow his girlfriend?
Answer: English Channel