This is a general depiction of the overall circulation. It is not detailed.
It takes dense salt water to make it work, not an ocean full of fresh water.
...In the Earth's polar (click title to entry - thank you) regions ocean water gets very cold, forming sea ice. As a consequence the surrounding seawater gets saltier, because when sea ice forms, the salt is left behind. As the seawater gets saltier, its density increases, and it starts to sink. Surface water is pulled in to replace the sinking water, which in turn eventually becomes cold and salty enough to sink. This initiates the deep-ocean currents driving the global conveyer belt....
This is the more detailed ocean circulation of the North Atlantic.
The Gulf Steam is a wind driven current and is warmer than most other currents in the Atlantic. It originates off Africa.
The North Atlantic Drift also known as the North Atlantic Current. It is a warm water current driven by the ocean conveyor belt. It is a considerable warming current to Europe.
