I do not see anything that would require you to hold an EASA license: the instructor is acting as a PIC and holds a valid EASA license. Per FAA regs you can log the flight time during the Flight Review as both Dual and PIC even if it is of foreign registry as long as the conditions below are met. Btw it is no longer called a BFR.
61.51
(j) Aircraft requirements for logging flight time. For a person to log flight time, the time must be acquired in an aircraft that is identified as an aircraft under § 61.5(b), and is -
(1) An aircraft of U.S. registry with either a standard or special airworthiness certificate;
(2) An aircraft of foreign registry with an airworthiness certificate that is approved by the aviation authority of a foreign country that is a Member State to the Convention on International Civil Aviation Organization;
..