Sitting for any exam is a stressful thing. The FE exam especially is a challenging one, which is why it's essential to choose the right timing and to book an appointment at the time that suits your schedule so it won't overlap with another important event in your life. Luckily, the NCEES organizes FE exams at different times of the year so that you can choose the right time for you. The exam is given each year in four testing two-months windows: January–February, April–May, July–August, and October–November. You can book your appointment in any period of the ones mentioned before. In the United States, the exam is given nationwide, and you have to check your state requirements before you apply for the exam. It is also offered in Canada, the Emirate of Sharjah (United Arab Emirates), Saudi Arabia, Qatar, Egypt, Japan, Taiwan, and Turkey. The NCEES is also working on adding new countries in Asia and the Middle East, where you can sit for the FE exam. If you have completed or enrolled in an ABET-accredited four-year engineering program, you are allowed to take the FE exam.
There are no restrictions on when you should take the exam, as you can take it during your senior year or after it. Most engineering students prefer to take the exam in their final semester in college as an undergraduate. However, it can be taken a bit earlier or after. If you are planning to sit for the exam after you graduate, it's better to do shortly after, as the exam covers the materials that are still fresh in your mind.
As the FE exam is organized during four two-month windows per year, you have plenty of time to decide what time suits you better. The most important is that you must be ready and fully prepared to pass an essential exam in your engineering career.