On the Plains of Abraham children are massing. School age, they gather in red tunics and blue tunics, and laugh as teachers line them up to face each other. Under a clear sky they shout oaths in French and English, and pretend to re-fight a battle, a battle that burns bright in the history of this fascinating city on the Saint Lawrence River.

It is a sunny day in early June, and the children have gathered in the large, expansive park of Plaines d'Abraham (The Plains of Abraham), which lies on the edge of the historic town, to learn about the battle, named after the field in which it took place, in 1759. The battle, remembered in both a nearby museum and in the city itself, was the defining clash between the French and the British empires in north America. For this writer, there was also a slight frisson involved in standing on the patch of earth. The Plains are mentioned in one of The Band's great songs, Acadian Driftwood, a song about the expulsion of the Acadians during the Seven Year's War. As Robbie Robertson tunefully noted, the British prevailed, but, as the drifts of history have passed, Quebec is once again dominated and demarcated by its French language, and its north American but distinct Francophone culture.

Quebec City is the capital of Quebec province. It is also, for European culture in the continent, old: there have been settlements on this picturesque rock which stands like a sentry over the river since 1608. Quebec itself means 'the narrows' – here the great river Saint Lawrence, so wide at times it seems from the air to be a sea, can be reasonably easily crossed. Today, that means regular ferries from one side to the other (indeed, a cheap ferry to the other side, a town called Levis, affords the best view of the city's beautiful outlook), but back in 1759 that meant that dastardly British army, under General Wolfe, could launch a sneak attack on the walled city.

Turbulent centuries later, the town walls still remain: handsome, medieval-style fortifications which surround the Old City and give the place a European, almost medieval air. The gates are thick, as in some towns in Europe, and you can walk along the top of the battlements. Indeed, with French as the primary language – it is polite to at least say hello in French when instigating conversations, and if you can speak more, all the better – it is easy to forget you are the other side of the Atlantic. With its stone-built architecture, fortifications, its intact, star-shaped castle called La Citadelle, the towering Chateau Frontenac Hotel and its elegant Second Empire-style parliament building, the city has the sense of a transplant direct from the old world.

And yet, of course, it is more than that: Quebec has a vibrant present and a fascinating, complex past. I flew to the city on a propeller plane on a short flight from Montreal, a big cosmopolitan city which can now be flown to directly from Glasgow. My courteous taxi driver to the centre of Quebec City, a short drive, was a Macdonald: many Scots, of course, made their way here across the Atlantic. He was eager to chat about the Scottish referendum, and also the European one.

Perhaps the best place to learn about the city and its place in Canadian and wider Quebec history is the excellent Musee de la Civilisation, down on Rue Dalhousie, not far from the oldest part of town. This gleaming institution has a eye-catching entrance – a large diorama of a boat caught in icebergs – while its displays efficiently and intelligently explain the history of Quebec, both the city and the region, from its founding by Samuel de Champlain.

Quebec City, rather like Edinburgh, is old, pre-industrial, and therefore walkable. It is not, as in some north American cities, primarily designed for cars, especially within the city walls. You can stroll the old streets within the walls for hours, and find touristy knick-knack shops, excellent coffee, fine food, lots of visual art of varying interest, and plentiful free wifi. Horse drawn carriages clip-clop the streets. You will spy brightly-painted tin roofs, and steep streets, old churches and quiet squares. There is a historic Scottish Kirk, and La Maison Simons was founded by the Simons family in 1840 and is among the oldest department stores in the city. There is a brand new gallery of modern art, also on the Plains of Abraham, with a new, futuristic wing, which has increased exhibition space substantially, as well as the national theatre.

If you want to appreciate some of the depth of the complex history of the city, and Quebec, take the vertiginous funicular down to the oldest part of town, right by the water's edge. It is here that Quebec City is at its oldest – and also most touristy. Shops are everywhere in the Petit Champlain district, from clothes to boutiques, selling hand-made wooden goods, furs, fudge, ice cream. The streets are lined with colourful shop signs that point to an older age.

The area's dedicated 'old time' feel could, in fact, be cloying to some, but the nearby Notre Dame des Victoires church is worth a visit. Established to celebrate a series of miraculous scrapes with misfortune which Quebec avoided it sits on the edge of a faithfully restored old square. And, whilst on the subject of religion, also worth a visit is the main Notre Dame de Quebec Basilica. Up the cliff from the old town, built in 1647, this site has been expanded, bombarded, burnt to the ground and rebuilt. But still it stands – the basilica itself is beautiful, including an extraordinary gold structure on three levels around the altar, and the only Holy Door outside Europe.

Near to the cathedral there is a great place to try one of Quebec's local dishes, poutine. The dish, the composition of which varies from place to place within Canada (and now comes in quite fancy versions with foie gras, if you like that kind of thing) is basically chips, cheese curds and gravy. It is commoners' food: peppery, filling, heartening and pretty tasty. I ate mine at the excellent Chic Shack (15 Rue du Fort, opposite the towering Frontenac) a friendly restaurant with outside seating.

Rue Saint Jean is one of the livelier boulevards. It is a fascinating street which runs both within and without the city walls. There are many bars, restaurants, book shops, antique stores and an unusual delicatessen. Epicerie Moisan, a capacious store which would not seem out of place in the depths of Monmartre or Lyon, stocks endless cheeses and meats, an extraordinary amount of herbal teas and drinks, fascinating cans and fruits, and more maple syrup than you can drown in. I purchased maple syrup lollipops here, maple syrup in cans for the long haul home, and far too much chocolate. Along the road is a fine little pub, with its own beers, called Le Projet. They serve poutine too (very good – but I suspect every bowl of poutine is), and in the relaxed, friendly bar – with some good Scottish whisky on its top shelf – you can relax and await the dimming of the day. I ate that night at Le Hobbit, a 'rustic chic' restaurant with deliciousness as a key note. The risotto was creamy and excellent, the wine better. Other eateries of note include Le Cercle, which has a large venue as well as a top restaurant (good vegetarian selections) and the more upscale but relaxed Brasserie SSS, in the Old Port.

If you have a head for heights, you could go up 31 floors of one of the city's few skyscrapers, to the Observatoire de la Capitale, which combines breath-taking views of the city and its surrounds, and also has an excellent timeline of both Quebec and the city on its walls, with video and sound. From this towering height you can see the majesty of the Saint Lawrence, taking boats, commercial and tourist, from the Atlantic into the heart of the north American continent, the rambling suburbs, and it may give you a taste, at least, of the scale of of Canada. And down below, the old, fascinating town clinging to its promontory – a navigable, pretty city, rich with culture and life.

Phil Miller flew to Quebec as a guest of Air Transat. It offers return flights from Glasgow to Montreal from £320 per person. For more information visit www.airtransat.com or call 00 800 872 672 83.

Tourisme Québec: For more information on visiting Quebec call 0800 051 7055.

email: info@quebecoriginal.com or visit: www.QuebecOriginal.com

Quebec City Tourism: www.quebecregion.com

Accommodation recommendation: www.hotelroyalwilliam.com/en/