I can't believe the pessimism here. He is not flying the Atlantic solo. He is planning a trip to Le Touquet.
OK, in amongst the doom and gloom is some good advice. Really do not go over water the first time in hazy conditions. You will scare yourself stupid, you will embarrass yourself in front of your girlfriend and you might kill yourself. Talk to someone who has just landed - it's almost impossible to judge from the ground.
Do obey the mass and balance to the pound. Not worth going outside despite the fact that most aircraft will happily fly heavy, especially when you can happily fly to Le Touquet from a few UK airfields in most PA28-161s with two male, two female modest-weight adults and land with more than an hour's fuel in the tanks. That gives reserves to divert if the runway is blocked and still land with 45 minutes gas - which puts you pretty much in IFR requirements for commercial flights!
Do plan that diversion even in great weather. The one in front has a gear collapse, blocks Le Touquet and suddenly you are really stressed, and mistakes happen.
I prefer the PA28 to the C172 - I just don't like the Cessna's dull handling, and don't see the point unless you are landing on a rough strip or need the downward visibility. PA28s always make you look better anyway, as all passengers judge you on the landing and it's easier to land well than the Cessna. Even better, as mentioned before, is a Robin DR400-180. The one I flew would carry full fuel and four 14-stone people, and hit 130 kts on a good day. However you will not easily find one to hire, and you will need a good check out. You might also need a map to find all the switches on the panel, due to completely random arrangement, and the cabin is tight for four people.
Think beforehand about emergencies. As soon as anything is wrong turn towards the nearest land and call MAYDAY. You can always cancel that later. Make sure everyone has lifejackets right in hand (try to get wearable ones) and knows how to use them, and not to inflate before leaving the aircraft. Dogsbody is pessimistic. People die landing wet, but most survive at least the initial touchdown and you will have plenty of ferries to help in the rescue. Ditch nearby but not in front, being run over by P&O is not funny.
Above all talk to your instructor before the flight. He will give you sound advice, more thorough than strangers on PPRuNe, and he will know whether you are up to this (some will be before even passing the PPL, some need more experience and a few should never cross a duck pond without an instructor). The trip is not hard, it is just different and a little more complicated.
Finally I repeat: don't do it unless the weather is great. Weather will kill you, not gross weight, navigation or technical problems.
Oh, and have fun!