Is it possible to get crema (i.e. the tan colored foam on top of espresso ) by using a french press?
I'm wondering if the beans need to be ground finely for crema to be achieved or if the way a french press works doesn't allow for it to happen.
To answer this it's important to understand what Crema actually is. Roasted coffee consists of somewhere around a thousand different substances, among which are aromatic oils, sugars, caffein, fiber and carbon dioxide trapped inside the beans.
Crema consists mainly of those oils, sugars, some proteins and importantly the CO2 gas trapped inside the bean. When an espresso machine pushes water through the grounds with high pressure, it emulsifies the fats/oils, dissolves some sugars and traps it all in little CO2 bubbles. The CO2 is forced out of the grounds through the high pressure. That's why you have considerably less crema if you use old, stale coffee. Because most of the CO2 trapped inside has evaporated already.
Now to your actual question. For the obvious reason, that is the lack of pressure in a French Press, Crema can not form. There can be some kind of foam, just as with pour overs, but it's not crema. It's not going to last long and will usually dissolve very quickly. If you were to create such a pressure in a French Press (which I highly doubt is technically even possible, since after all you want to brewed coffee to go through the mesh filter, but not the grounds), you would likely have crema forming on the bottom where the grounds settled and then rising to the top, just as it does when you pull a shot of espresso. Order an espresso shot in a transparent shot glass once and observe how the coffee flows out in the beginning as a mixture of coffee and crema and then observe the crema rising to the top, I heard people call it Guinness effect.