The IRS says that U.S. citizens and resident aliens abroad generally must file income-tax returns in the same manner as those in the United States when the filing rules are met. Gross-income calculations may include income that is later excluded under the FEIE, so the filing question should be assessed before choosing the relief method.
Form 1040 is the central return, but the final package may also require schedules, Form 2555, Form 1116, Form 8938, an FBAR or other forms depending on the facts.