The question cites two specific Contract Procurement Instrument Identifiers (PIIDS) -- Instruments C and F -- which are listed the Federal Acquisition Regulations (FAR) Subpart 4.16 in paragraph 4.1603.

C - General (Contracts of All Types)

F - Task Orders, Delivery Orders, or Calls under Indefinite Delivery contracts (Instrument D), Blanket Purchase Agreements (Instrument A) and Basic Ordering Agreements (Instrument G).

However, the type of FAR Contract Instrument used for FMS is generally a secondary consideration.

The primary consideration in chosing the optimal FMS contracting approach would be whether a fixed price contract (there are various types) or a cost plus contract (there are various types) should be used.  This decision is normally based on how well defined the defense articles and services are.  Fixed price-type contracts are generally used to acquire both DoD domestic and FMS defense articles and services that are well defined, have a known procurement history, and are subject to full and open competition.  Cost plus-type contracts are generally used when DoD domestic and FMS defense articles and services are being developed and/or the articles and services desired are difficult to define or specify.

DAU recommends you consult with your contracting organization regarding the best type of contractual approach (fixed price (FP) versus cost plus (CP)) and optimal contractual instrument (which are listed FAR Subpart 4.16) for the FMS defense articles and services described in the FMS Letter of Offer and Acceptance (LOA) signed with the customer country.

In most cases, DoD acquisition organizations use the same contractual approach (FP or CP) and contractual instrument type for FMS acquisitions that they would use for identical or similar DoD domestic accquisitions.

Added 3/31/2020:  Please also see the DoD Class Deviation 2018-O0017 Determining Contract Type for FMS Contracts, dated 29 Jun 2018.