A small, brave band of adventurers have crossed the ocean to a distant continent. These pioneers stumble across a mass ritual execution of those charged with crimes against the region’s tribal gods. One unfortunate will even be burnt at the stake after an accusation of “cooking with olive oil instead of lard”. Aghast, the Inca voyagers watch in 1530s Toledo as the Inquisition prepares an auto-da-fé that will commit suspected Jews, Muslims, heretics and witches to the flames. Surely the brutes who rule this “hostile land” deserve no mercy? The terrified visitors from the Andes massacre the Christians — who find that “their nailed god was no help at all”.

Laurent Binet is the French novelist who turned the assassination of Nazi leader Reinhard Heydrich into a meta-historical fantasia with his 2010 debut HHhH. In The Seventh Function of Language, he blended Left Bank campus farce and literary parody into a thriller-like quest for a linguistic superpower supposed to have been discovered by the theorist Roland Barthes. In Civilisations, Binet unites an Enlightenment-style critique of European follies from afar with the counterfactual storyteller’s upside-down history. The result is a third high-concept romp, although his re-engineered version of the past also surely owes a debt to the alternative-world scenarios beloved by grand-strategy video gamers.

Like authors and games developers before him, from Christopher Evans’s 1993 novel Aztec Century to the Europa Universalis games, Binet dwells on the “what ifs?” of Columbus’s expedition in 1492 and its aftermath. Here, the Genoese chancer fails, and is captured by the Caribbean Tainos. However, a saga-like prologue has informed us that, around the year 1000, the Vikings of Vinland moved south into Central America, led by their warrior queen Freydis. That prior incursion will have world-shaking consequences. Now, in 1531, civil war in the Inca Empire drives the co-ruler Atahualpa north, first to Cuba and then east across the “ocean sea”. He arrives in Lisbon accompanied by the diplomatically astute Cuban princess Higuénamota, 181 other companions, 37 horses — yes, decisively, these Incas possess them — and a ceremonial puma.

That turns out to be enough. Impossible? Look at Cortés’s and Pizarro’s odds-defying conquests. The emperor and princess adroitly exploit an environmental catastrophe (Binet shunts the Lisbon earthquake of 1755 backwards in time), pestilence, doctrinal strife and an external threat from the Ottoman Turks. Atahualpa soon becomes regent of Spain. He plants its wastelands with potatoes, quinoa and maize, while abundant Inca gold and silver turn Seville into “the axis of the world”. By the early 1540s, only a few German pacts and battles stand in the way of the Inca’s election as Holy Roman Emperor.

Atahualpa, Son of the Sun, considers Christian baptism a mere trifle. Martin Luther himself argues that the Inca religion may simply be “a version of the Gospel designed for the world beyond the seas”. In a novel rich in playful literary pastiches — of Norse sagas, Renaissance verse epics, Spanish chronicles, all captured with eloquent dexterity by translator Sam Taylor — Binet also gives us Thomas More’s correspondence on the Incas with Erasmus. Don’t dismiss the incomers as heathens, the Dutchman writes to More; their rise to power may be “a stroke of fortune” that opens the door into the “Europe of tolerance” both scholars desire. Indeed, Atahualpa’s “Seville Edict” blesses other faiths so long as worship of the Sun takes precedence.

So Europe briefly enters an Inca-led “episode of happiness”. A storm brews, however, over the ocean. In Mexico, the Aztecs also discover a taste for epic seafaring. Here, Binet overreaches himself. Too much happens too fast to allow more than an overstuffed recital of imaginary chronologies. The laborious pile-up of alternative facts renders this phase of Civilisations clogged and inert. Yet the mischievous wit of Binet’s premise never quite forsakes him. Counterfactual fictions often show that you can switch the poles of the past and still finish in much the same place. So it is here: Henry VIII converts to the Inca faith, England’s monasteries become Temples of the Sun, and poor Thomas More ends up in the Tower — as in our familiar past — appalled at “these incredible blasphemies”.

As if bored, Binet gives up on his chronicle. He closes with a Tom Stoppard-esque sequence in which Montaigne, Cervantes and El Greco talk art, faith and tolerance in Montaigne’s manor near Bordeaux. That great sceptic’s genial insistence that “no belief offends me, whatever contrast it offers with my own” touches the novel’s core. The dismal real history of Europe’s snail’s-pace progress towards diversity in faith and culture gives Binet’s Inca-ruled dreamworld its true focus. Civilisations abounds in bold ideas, but has trouble making some of them stick — a problem, after all, that has plagued empire-builders throughout history.

Civilisations, by Laurent Binet, translated by Sam Taylor, Harvill Secker, RRP£16.99/Farrar, Straus and Giroux, RRP$27, 320 pages

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