For this to happen, you would need more monarchies to more active in retaining their influence whilst simultaneously being more accepting of their colonies becoming independent. The idea of personal union is a justifiable concept, even in post-colonial states, as states sharing monarchs is an ancient idea. So countries gaining independence, such as from the UK, were to willing to acquiese to retaining the monarch. Republics sharing the same head of state is nearly indefensible as a proposition. Which means a post-colonial commonwealth centered around France has so many problems to overcome, it might as well not exist. The French community was destined to failed since it amounted to France asking its ex-colonies voluntarily signing up to be Protectorates; unsurprisingly no country de facto took up France's offer.
So my version of this ATL, it would first focus on the other colonial powers besides France and the UK.
The Netherlands is a first candidate. Right off the bat, Indonesia is not going to retain the monarch. The colonial war was anearly unavoidable event and by the time the Dutch monarch along with the political establishment would want to negotiate an independence that would keep the monarch; too much blood had been spilt by Indonesia for this union to last.
So the Netherlands' Caribbean colonies would comprise this Commonwealth. This ATL's POD is that the Dutch government, still shaken by the Indonesian war and seeing their Caribbean colonies asking for independence, decide to negotiate their independence around the mid 50s. One of their terms is that they retain the Dutch crown in personal union with the Netherlands. This Dutch Commonwealth takes the places of what the Dutch did in the OTL which was essentially copy the UK's model of constituent countries and annex their colonies.
The second country to form a commonwealth is Portugal. The POD of this is that Salazar relies more heavily on monarchists to gain power, so as a concession, he restores the monarchy in a ceremonial role. Portugal became engaged several colonial wars in Africa towards the end of Salazar's life. In the OTL, once Salazar died, the regime he set up started going downhill due to being bogged down by many crises caused by the colonial wars. In the ATL, once Salazar dies, the nominally constitutional monarch intervenes in politics; he publicly backs calls to negotiate an end to the wars. This leads to a pro-peace faction within the regime taking power. As part of the negotiations for independence, Portugal hands over power to anti-communist groups. A condition for Portugal granting independence is that the countries keep the monarch. This happens in the late 60s to 1970.
