It turns out it happened at least twice in relation to Namibia and respectively South Africa, as a 1975 report says
The mailing says the USA, Britain and France today exercised their veto power in the United Nations Security Council in behalf of South Africa and against an assertion of UN rights in Namibia and of the rights of the Namibian people to their freedom and independence; the big three teamed together again - as they did on 30 October 1974 when they thwarted South Africa's expulsion from the UN - to cast the second triple veto in the history of the world body; the three Western permanent members rejected a mandatory arms embargo
A 2014 article mentions there were 13 triple vetoes and 16 double ones, without further details.
FWTW, more recently Iran has claimed that Russia, China, and Algeria proposed to condemn the Israeli attack on the Iranian embassy in Damascus, but that the US, UK, and France blocked that statement (which I'm not if it was actually a proposed resolution). A bit more searching found a Reuters story on that:
The United States, Britain and France on Wednesday opposed a Russian-drafted U.N. Security Council statement that would have condemned an attack on Iran's embassy compound in Syria, which Tehran has blamed on Washington's ally Israel.
Press statements by the 15-member council have to be agreed by consensus. [...] The U.N. Security Council has issued statements in the past condemning attacks on diplomatic premises.
TBH I'm not sure on the practical diff between a statement and a resolution [merely] condemning something, other than the former not being entered in UN annals in a certain way, I guess.
OTOH the same source says that the EU did condemn the strike, so I guess there was some diff in wording that France didn't like in the Russian proposal.