To grow nice straight carrots is something a lot of home gardeners find troublesome. I have grown them successfully plenty of times: on the Facebook page I have videos of the carrots I have grown - nice straight and actually easy to grow.
The secret is (and it isn't really a secret) to use sand. I lay good compost in a deep trench and then back fill it with sand (or a really sandy mix of soil) and then lay a thin sprinkle of good compost on top to strike the seed. Then plant your seeds.
A simple trick to getting a good spacing as the carrot seeds are so fine is to use some paper towel torn into strips and then use a cotton bud to dab honey onto it at the required spaces. The seed will stick to the honey, the excess falls off, then lay the strip into place and sprinkle a light layer of soil over it. Water in and wait for the results.
I actually don't worry too much about spacing, I just broadcast the seed liberally along the trench. As the carrots grow I thin them out using the hose to wet the area thoroughly and tease out the chosen plant leaving the rest to continue to grow larger. This also helps to assist in a longer harvest which can also be extended by succession planting.
The carrots seem to strike and then plunge their way to the good stuff before becoming plumper by the week as they expand unhindered by the sand but fed by the compost they strived to reach. It has served me well using this method, give it a crack and see what results you can achieve.
Image: Evan-Amos, Public domain, via Wikimedia Commons