Not necessarily. Aircraft built before some cutoff date (1974?) may keep
the CF-XXX style of registration if they wish. I think that you still
appear in the TC database as C-FXXX.

Here's what CAR 202.03 says:

202.03 (1) Subject to subsection (2), the nationality mark in respect
of a Canadian aircraft is the letter "C" and the registration mark in
respect of the aircraft is a combination of four letters specified by
the Minister.
(2) Subject to subsection (3), where an aircraft was registered in
Canada before January 1, 1974 or is a vintage aircraft,
(a) the nationality mark in respect of the aircraft is the letters "CF"
and the registration mark in respect of the aircraft is a combination
of three letters specified by the Minister; or
(b) the nationality mark in respect of the aircraft is the letter "C"
and the registration mark in respect of the aircraft is a combination
of four letters specified by the Minister.
(3) Where the owner of an aircraft, other than a vintage aircraft, that
has the letters "CF" as its nationality mark and a combination of three
letters as its registration mark repaints the aircraft, the owner
shall, prior to operating the aircraft, change the nationality mark to
the letter "C" and the registration mark to the letter "F" followed by
the combination of three letters.
(4) Where the owner of an aircraft changes its marks pursuant to
subsection (3) or the owner of a vintage aircraft changes its
nationality mark from "C" to "CF" or from "CF" to "C", followed by the
appropriate registration mark, the owner shall, prior to operating the
aircraft, notify the Minister in writing of the change, and the
Minister shall change the marks accordingly in the Canadian Civil
Aircraft Register and issue a new registration certificate to reflect
the change.

According to section (3), vintage aircraft can keep the old marks.
Here's their definition of vintage:

"vintage aircraft" - means an aircraft that was manufactured prior to
January 1, 1957. (CAR 200.01)

You were right: there are exceptions for old airplanes. There are
still compassionate people in government!

Dan