Here in the U.S., we can use a herbicide containing Trifluralin as a preemergent herbicide in carrots. One brand name here is Treflan. This should be applied to a tilled seed bed well before planting the carrots, (at least a week) but before the emergence of weeds.
Most advice on planting carrots is to have the seedlines or rows about 12 to 18 inches apart. I've had far better luck planting them only 6 inches apart. When they do germinate and begin to grow the shade the space between the rows better and controls late emerging weeds.
Here, several seed companies sell carrot, beet, radish and even lettuce seeds implanted on a dissolvable paper tape about 15 feet long. The seeds are evenly spaced and I've had good luck with them for many years. They are, perhaps, no more than 10% more expensive than a packet of seeds, most of which are lost or discarded. Another advantage of the seed tapes is the ability to more easily plant suceeding crops after the firs thave germinated to provide late season harvest of both beets and carrots.
Best of luck!