CANZUK

[Furunculus]

AFAIK Australia and New Zealand are already regional powers, with Australia looking towards SE Asia and New Zealand at SW Pacific. The UK isn't going to be joining anything there, and they don't need the UK to be a power in these regions. If anything, Australia are more likely to break further away from the existing tenuous political links with the UK. And if Australia need military backup in any confrontation in that region; Singapore is the signal lesson. And the UK is further reducing its military.

I always like to start from that nebulous construct: the great power.
Which I have always defined as a Middle power ** that is also a Regional power *** [and] without polar opposition within its own region.

So Canada would be a good example of a Middle power, but I would not consider it a Regional power.
India, for example, is a good example of a Regional Power, that is also a Middle Power.
However, that last part of my definition is important, because the resource required to contest and control its polar opposition within its own region, prevents it being considered a Great Power.
I would consider France and Britain to be Great Powers, though both are hanging in there by the skin of their teeth (particularly france!).

Do Australia and NZ (and the other FPDA countries) have an interest in seeking alliance with France and Great Britain?

The answer to that depends on whether they follow the eastern or the western method of geopolitics.
Bandwagoning or Balancing:
The east tends to be characterised by Bandwagoning - where the emergence of a new Regional hegemon results in lesser powers falling into its orbit, and following its geopolitical preferences.
Hence America has an absolute need to support Taiwan and Korea, because if it was seen to falter on either one it would likely lose both, then Japan would follow, and Asia would be entirely within the orbit of China.
The west tends to be characterised by Balancing - where the emergence of a new Regional hegemon results in a coalescence of lesser powers against the hegemon, often bringing in outside support.
The best example here is the european wars of the 19th Century. The triple-entente, the entente-cordiale, the anglo-polish agreement. Roping in America to swing the outcome on both occasions.

So, how do Australia and NZ respond to the rise of China?
I would say they are firmly in the Balancing category:

Cooperation between the United States, Japan, Australia, and India is here to stay:
https://thediplomat.com/2017/11/take...-quad-is-back/

The durian pact: the Five Power Defence Arrangements:
https://www.aspistrategist.org.au/du...-arrangements/

The Importance of Australia to the United States:
https://geopoliticalfutures.com/the-...united-states/

So, to wheel this back around to the original question mark about Britain's utility to Australia:

Does Australia want the active support of one of the worlds few real Great Powers, that possesses the worlds second most capable expeditionary military function, and has demonstrated time and time again a willingness to employ it for elective warfare?

Unless they are clearly lost possession of their faculties, YES!
Does the same hold true for Japan, and the other FPDA countries? Yes it does.

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http://www.oxfordbibliographies.com/...43292-0222.xml

** "middle powers can be distinguished from superpowers and smaller powers because of their foreign policy behaviour – middle powers carve out a niche for themselves by pursuing a narrow range and particular types of foreign policy interest. In this way middle powers are countries that use their relative diplomatic skills in the service of international peace and stability."

*** "A regional power is a state that projects influence in a specific region. If this power capability is unrivaled in its region, the state could rise to the level of a regional hegemon. The regional powers display comparatively high military, economic, political, and ideological capabilities enabling them to shape their regional security agenda."