UNITED STATES
SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 6-K

REPORT OF FOREIGN PRIVATE ISSUER PURSUANT TO RULE 13A-16 OR 15D-16 UNDER THE

SECURITIES EXCHANGE ACT OF 1934

For the month of June, 2020

Commission File Number 32297

CPFL Energy Incorporated

(Translation of Registrant's name into English)

Rua Jorge de Figueiredo Correa, nº 1632, parte
CEP 13087-397 - Jardim Professora Tarcilla, Campinas – SP
Federative Republic of Brazil

(Address of principal executive office)

Indicate by check mark whether the registrant files or will file annual reports under cover Form 20-F or Form 40-F. Form 20-F ___X___ Form 40-F _______

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(1): [ ]

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(7): [ ]

Indicate by check mark whether the registrant by furnishing the information contained in this Form is also thereby furnishing the information to the Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.

Yes _______ No ___X____

If "Yes" is marked, indicate below the file number assigned to the registrant in connection with Rule 12g3-2(b): 82-_________________

CPFL ENERGIA S.A.

Publicly-held Company

CNPJ 02.429.144/0001-93 - NIRE 353.001.861-33

CPFL GERAÇÃO DE ENERGIA S.A.

Publicly-held Company

CNPJ 03.953.509/0001-47 - NIRE 353.001.795-95

MATERIAL FACT

CPFL Energia S.A. (“CPFL-E”) and CPFL Geração de Energia S.A. (“CPFL Geração” and, with CPFL-E jointly referred to as “Companies”), pursuant to article 157, §4º of Law No. 6.404/76 (“Law 6.404/76”) and the CVM Instruction No. 358/02, in addition to the Material Facts disclosed on November 19^th, 2019, April 28^th, 2020, May 6^th, 2020, and May 21^st, 2020, within the scope of the tender offer for the acquisition of the common shares, which remain outstanding, issued by CPFL Energias Renováveis S.A. (“CPFL-R”), unifying the modalities for the purpose of converting its register as a publicly-held company in category “A” to category “B” (“Register Conversion Offer”) and its Novo Mercado delisting (“Novo Mercado Delisting Offer”, and, with the Register Conversion Offer, jointly referred to as “DTO”), hereby inform its shareholders and the market in general that final acquisition price for the DTO’s Auction, after the adjustments provided for in item 4.5 of the Notice of Tender Offer, is BRL 18.24 (eighteen reais and twenty-four cents) per common share, to be fully paid on the Settlement Date.

The Companies shall keep its shareholders and the market informed on the progress of the subject matter informed herein.

Campinas, June 5, 2020.

YueHui Pan

Chief Financial and Investor Relations Officer

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

Date: June 5, 2020

CPFL ENERGIA S.A.

	By:	/S/ YueHui Pan
	Name: Title:	YueHui Pan Chief Financial Officer and Head of Investor Relations

FORWARD-LOOKING STATEMENTS

This press release may contain forward-looking statements. These statements are statements that are not historical facts, and are based on management's current view and estimates of future economic circumstances, industry conditions, company performance and financial results. The words "anticipates", "believes", "estimates", "expects", "plans" and similar expressions, as they relate to the company, are intended to identify forward-looking statements. Statements regarding the declaration or payment of dividends, the implementation of principal operating and financing strategies and capital expenditure plans, the direction of future operations and the factors or trends affecting financial condition, liquidity or results of operations are examples of forward-looking statements. Such statements reflect the current views of management and are subject to a number of risks and uncertainties. There is no guarantee that the expected events, trends or results will actually occur. The statements are based on many assumptions and factors, including general economic and market conditions, industry conditions, and operating factors. Any changes in such assumptions or factors could cause actual results to differ materially from current expectations.

CPFL Energy INC 6-K