The former Prime Minister said his view was based on several talks with senior EU leaders.
Mr Brown also said that the country is being torn into pieces by "competing nationalisms" and that reconciliation will take "years if not decades".
The ex-Labour MP also said he hoped it give MPs more time to pass emergency legislation, The Herald reported.
He said President Macron had demanded a six month extension rather than a year to “sound tough” to a domestic audience six weeks before the European elections.
Speaking at the inaugural meeting of the Our Scottish Future think tank in Edinburgh Mr Brown said: "We meet at the end of a week which has triggered the biggest peace-time constitutional crisis in recent history - an ugly battle between a sovereign Parliament and a government claiming it is a non-sovereign Parliament - with questions being raised not just about what kind of Brexit but what kind of Britain.
"This is now about the very survival of the United Kingdom.
"Only four weeks into his premiership, Boris Johnson is not only shredding our constitution but tearing the country apart with no plan to bring people together again and no unifying national project to ever do so.
"Leadership should be about healing divisions and not accentuating them.
"But today I see a Britain that has never been so divided - Leavers versus Remainers, north versus south, cities versus towns, young versus older - a Britain now being broken into pieces by competing nationalisms.
"We now have Scotland-first nationalism, England-first, Northern Ireland-first and Wales-first nationalisms - all challenging the very idea of one United Kingdom and creating divisions so deep that reconciliation will take years if not decades of soul searching to repair the damage being done."
Mr Brown also said that Scotland is being presented with two "extreme and divisive options", neither of which meets the "needs and aspirations" of the Scottish people, the majority of whom want Scotland in both Britain and Europe.
He said: "Scotland is now trapped between two nationalisms - Boris Johnson's, which is anti-European and ignoring Scotland's interests - and Nicola Sturgeon's, which is now so hardline that she now proposes - a big shift from their 2014 referendum position - to exit the UK customs union, abandon the UK single market and ditch the UK pound.
"As we think of the future of Scotland we have to stand back and ask what is a far more fundamental question: What constitutional option best meets the needs and aspirations of the Scottish people?"
Our Scottish Future will examine what all of the possible constitutional options mean for the living standards, public services and livelihoods of the people of Scotland and the impact they would have on poverty, the NHS and schools.
The seminar on Friday will examine the four currency options for Scotland.