Under North Carolina law § 14-415.12. Criteria to qualify for the issuance of a permit
(b) The sheriff shall deny a permit to an applicant who:
(1) Is ineligible to own, possess, or receive a firearm under the provisions of State or federal law.
(2) Is under indictment or against whom a finding of probable cause exists for a felony.
(3) Has been adjudicated guilty in any court of a felony.
(4) Is a fugitive from justice.
(5) Is an unlawful user of, or addicted to marijuana, alcohol, or any depressant, stimulant, or narcotic drug, or any other controlled substance as defined in 21 U.S.C. § 802.
(6) Is currently, or has been previously adjudicated by a court or administratively determined by a governmental agency whose decisions are subject to judicial review to be, lacking mental capacity or mentally ill. Receipt of previous consultative services or outpatient treatment alone shall not disqualify an applicant under this subdivision.
(7) Is or has been discharged from the armed forces under conditions other than honorable.
(8) Is or has been adjudicated guilty of or received a prayer for judgment continued or suspended sentence for one or more crimes of violence constituting a misdemeanor, including but not limited to, a violation of a misdemeanor under Article 8 of Chapter 14 of the General Statutes, or a violation of a misdemeanor under G.S. 14-225.2, 14-226.1, 14-258.1, 14-269.2, 14-269.3, 14-269.4, 14-269.6, 14-276.1, 14-277, 14-277.1, 14-277.2, 14-277.3, 14-281.1, 14-283, 14-288.2, 14-288.4(a)(1) or (2), 14-288.6, 14-288.9, 14-288.12, 14-288.13, 14-288.14, 14-318.2, 14-415.21(b), or 14-415.26(d).
(9) Has had entry of a prayer for judgment continued for a criminal offense which would disqualify the person from obtaining a concealed handgun permit.
(10) Is free on bond or personal recognizance pending trial, appeal, or sentencing for a crime which would disqualify him from obtaining a concealed handgun permit.
(11) Has been convicted of an impaired driving offense under G.S. 20-138.1, 20-138.2, or 20-138.3 within three years prior to the date on which the application is submitted.
From what I can tell, simple assault is a Class 2 misdemeanor. Therefore, it may be considered a crime of violence under subsection 8 and disqualify you from obtaining a permit. You may wish to contact your local police department to see how a simple assault is viewed in relation to the permit.
I hope that helps. Please let me know if you have additional questions.