Excessively sour flavor in your coffee brew is a likely sign of underextraction, i.e. the coffee has not brewed long enough and has an excess of acids. Acids are extracted early in the brewing process, whereas other balancing flavors are extracted later in the process.
[The coffee is] "under-extracted", specifically "under-developed" – desirable components have not been sufficiently extracted – and "unbalanced", specifically sour, because acids are extracted early, while balancing sugars (sweetness) and bitter components are extracted later.
Making good coffee involves a multitude of factors, and it can take some trial & error to hit the sweet spot. But let's mention the major ones:
Yields depend primarily on temperature, brew time, and grind size, and in a complex way on method.
For your case, I'll just call out the most obvious thing: Because you're using a French press, you have to use a coarser grind than something like a drip machine requires. Those larger coffee grains are going to require more extraction time.
So it could be that it simply needs to steep a little longer before pushing down the plunger. I personally like to give my coffee a stir for about a minute after pouring in the water to help encourage thorough extraction.
Hopefully some experimentation along those lines will help you achieve the perfect cup. Happy caffeinating!