On cursory reading your quote of EO 12139
appears to give the President carte blanche to
carry on surveillance without court approval. However sections 1-101 and 1-104 of this EO are not creating new law or doing away with existing law. It appears to merely expand on the President’s authority BUT STILL WITHIN AND CONTROLLED by FISA [50 U.S.C. section 1802].

Here:

EO 12139
1-101. Pursuant to Section 102(a)(1) of the Foreign Intelligence
Surveillance Act of 1978 (50 U.S.C. 1802(a)), the Attorney General
is authorized to approve electronic surveillance to acquire foreign
intelligence information without a court order, but only if the
Attorney General makes the certifications required by that Section.

1-104. Section 2-202 of Executive Order No. 12036 (set out under
section 401 of this title) is amended by inserting the following at
the end of that section: ”Any electronic surveillance, as defined
in the Foreign Intelligence Surveillance Act of 1978, shall be
conducted in accordance with that Act as well as this Order.”

and here:

Section 1802. Electronic surveillance authorization without court order; certification by Attorney General; reports to Congressional committees; transmittal under seal; duties and compensation of communication common carrier; applications; jurisdiction of court

(a)(1) Notwithstanding any other law, the President, through the
Attorney General, may authorize electronic surveillance without a
court order under this subchapter to acquire foreign intelligence
information for periods of up to one year if the Attorney General
certifies in writing under oath that -
(A) the electronic surveillance is solely directed at -
(i) the acquisition of the contents of communications
transmitted by means of communications used exclusively between
or among foreign powers, as defined in section 1801(a)(1), (2),
or (3) of this title; or
(ii) the acquisition of technical intelligence, other than
the spoken communications of individuals, from property or
premises under the open and exclusive control of a foreign
power, as defined in section 1801(a)(1), (2), or (3) of this
title;
(B) there is no substantial likelihood that the surveillance
will acquire the contents of any communication to which a United
States person is a party; and
(C) the proposed minimization procedures with respect to such
surveillance meet the definition of minimization procedures under
section 1801(h) of this title; and…

The administration still has a lot of explaining to do. At least for now we still are a country of laws. Americans, including the President, can’t just trample on laws we do not like in the name of expediency and of nebulous talking points as the so called “war on terror”

EXERCISE OF CERTAIN AUTHORITY RESPECTING ELECTRONIC SURVEILLANCE
EO 12139
23 May 1979

“By the authority vested in me as President by Sections 102 and
104 of the Foreign Intelligence Surveillance Act of 1978 (50 U.S.C.
1802 and 1804), in order to provide as set forth in that Act (this
chapter) for the authorization of electronic surveillance for
foreign intelligence purposes, it is hereby ordered as follows:

1-101. Pursuant to Section 102(a)(1) of the Foreign Intelligence
Surveillance Act of 1978 (50 U.S.C. 1802(a)), the Attorney General
is authorized to approve electronic surveillance to acquire foreign
intelligence information without a court order, but only if the
Attorney General makes the certifications required by that Section….”

http://www.fas.org/irp/offdocs/eo12139.htm

Note this is an order to acquire “foreign intelligence” with no other limits. It neither limits the surveillance to foreign nationals nor does it limit it geographically. Apparently you acquire “foreign intelligence” from anyone, anywhere.