Do I need Calculus 3 before learning Fourier series?

You usually do not need all of Calculus 3 to start Fourier series. The most important prerequisites are: - integration, - trigonometric identities, - infinite series basics, - comfort with functions on intervals, - some differential equations if you want applications. Calculus 3 helps later, especially when Fourier methods appear in multivariable PDEs, vector calculus, or higher-dimensional problems. But for a first Fourier series course, Calculus 2 is often enough if you can compute integrals like $$\int_{-\pi}^{\pi} f(x)\sin(nx)\,dx$$ and $$\int_{-\pi}^{\pi} f(x)\cos(nx)\,dx.$$ So the short answer is: no, not always. Review integration and trig first. Learn Calculus 3 if your Fourier course moves into PDEs or physics.