Square meals: Potagers are vegetable gardens taken to their ultimate geometrical conclusion. And they look just too good to eat, says Anna Pavord

Potager, like bidet and treillage, is a word that hovers uneasily on the outskirts of our language.

It's too Frenchified to use without feeling self-conscious.

Hors d'oeuvre, already bandied about by Pope and Smollett in the middle of the 18th century, is an easier proposition. It's been with us longer and there's no precise equivalent in English to replace it. For the same reason we have to get our tongues round potager.

Used the English way, it means posh veg, grown as part of a formal design, mixed up with flowers and fruit and whatever else makes them look decorative as well as useful. In English cottage gardens, flowers and vegetables have been growing together for centuries, mostly by accident. The potager replaces randomness with order.

Villandry, the great renaissance château west of Tours in France, has the world's most famous potager, acres of it, divided into nine equal squares, each containing a different design of formal beds edged in box. The thought of actually eating any of the vegetables in the vast potager at Villandry is quite shocking. Rich ruby chard, metallic blue leeks, shining parsley and frilly lettuce in bronze and green are used like richly textured paint. It's a work of art. Getting the geometric patterns in the beds to work together once a year is achievment enough, but the gardeners here plant this section twice a year, using different crops each time, one lot for late spring, another for late summer.

Although it looks as authentically old as the château itself, the potager at Villandry is a 20th-century invention, a pastiche, based on engravings of gardens made in the 16th century by Jacques Androuet du Cerceau. It's a wonderfully preposterous place, the formal, symmetrical design softened by billowing arbours of roses set at the intersections of the paths. Around the walls are beautifully trained fruit trees, made into forms that we don't see much in our own kitchen gardens: three-pronged Neptune tridents, elegant bowls the shape of wine glasses.

The scale is what makes Villandry so overwhelming. The gardeners here raise 60,000 vegetable plants, another 45,000 bedding plants (verbena, rudbeckia, forget-me-nots, fat double daisies) for the narrow flower borders that surround the major squares in the design. Ten thousand tulips are planted for the first spring display. Once the summer vegetables have been planted - pumpkins, squash, aubergines, tomatoes as well as the leafy vegetables that give the potager its bulk - the gardeners start clipping the three miles of box hedging that edge the beds.

The 17th-century Potager du Roi at Versailles is completely authentic. It was designed by Louis XIV's head gardener, Jean de la Quintinie who wrote that he was 'so convinced of the innocent pleasure given by the sight of a handsome potager that in all large gardens I recommend building a pavilion, not merely to provide shelter in storms ... but also for the pleasure derived from admiring in comfort land that is well used'.

Louis XIV had a passion for figs and there were 700 fig trees in his potager, carefully managed against walls and under glass to crop for six months of the year. In a technical sense, the gardeners in the potager were the pioneers of their craft. Internal walls of the potager (most are now gone) were carefully angled to catch sun at every possible hour of the day. Vast quantities of farmyard manure were heaped up to make the hotbeds that produced early crops of strawberries and salads. If the king wanted lettuce in January, he could have it. And asparagus by March, thanks to the gentle forcing that the hotbeds encouraged. Six thousand asparagus plants were lined up to feed the court.

Like Villandry, the Potager du Roi - it covers 22 acres - is laid out in a formal design. At the centre is a sunken square surrounding a circular pool with a water jet. Round the walls are the glasshouses where armies of gardeners grew melons, pineapples, peaches, apricots and all the other swanky fruit necessary for the king's table. The glass came from the factory at Saint Gobain; glasshouses, heated by woodburning stoves, revolutionised the way that gardeners produced fruit and vegetables in the potager.

On a slightly more domestic scale (though still covering more than two acres) is the potager made by the Comtesse de Saint Venant at the Château de Valmer in the Loire. Two wide paths of crushed hoggin divide the potager into four squares with a round pond at the centre. In the box-edged beds are vast collections of herbs - mint, basil, thyme - and the vegetables that commercial growers have mostly forgotten: strangely shaped aubergines and tomatoes, more than a hundred different kinds of lettuce, beans with evocative names such as 'Nombril de Bonne Soueur' (it means nun's navel).

As in other potagers in France, great use is made of trained fruit trees. At Valmer, you'll find ancient varieties of apple carefully pruned into espaliers and fans to divide up the space, as well as provide a fine autumn harvest. In autumn too, the gourd tunnel is at its best, two hundred metres of it, built from chestnut poles and hung with bizarre gourds swinging like lanterns. The French have never let go of Jean de la Quintinie's idea that a handsome potager gives at least as much pleasure as a border of flowers.

Gardens to visit in France

Villandry, 37510 Villandry (18km west of Tours) is open daily (9am-5pm). Admission €5.50. Call 00 33 2 47 50 02 09, e-mail info@chateauvillandry. com or visit www.chateau villandry.com

The Potager du Roi at ENSP 10, Rue de Marechal Joffre, 78000 Versailles (22km west of Paris) is open from Tues-Sun (10am-6pm) until the end of October. From Nov-Mar it is open Tues-Fri. Admission weekends €6.50, weekdays €4.50. Fruit and vegetables from the potager are sold there every Tues and Fri from 8.30-11.30am. Call 00 33 1 39 24 62 62 or visit www.potager-du-roi.com

The Château de Valmer, Chancay, 37210 Vouvray, is open Sat-Sun (10am-12.30pm and 2pm-6pm) in May-June, Tues-Sun (10am-7pm) in Jul-Aug, Tues-Sun (10am-12.30pm and 2-6pm) from Sept to 7 October. In Basse Normandie, there is a small potager attached to the 13th-century Benedictine Priory, the Prieuré Saint-Michel, at Crouttes, 61120 Vimoutiers, planted with medicinal plants as well as vegetables. The priory is run as an inn andyou can stay there (double room €110) or rent the old bakery (€650 a week). Dinner is €25. Wander round the potager with a glass of wine first. Visit www. frenchwayoflife. net.

In Haute Normandie, look for Miromesnil, the château where Guy de Maupassant was born. The walled kitchen garden is still planted in the traditional way, with ribbons of peonies under the old apple trees. The château is at Tourvillesur-Arques, 76550 Offranville. It's open daily (2-6pm) from April until the end of October. Admission €6.50. Call 00 33 2 35 04 44 47, e-mail miromesnil@ chateaux-france.com or visit www.chateaux-france.com .

In the Ile de France, the plant shows at St Jean de Beauregard draw chic Parisiens as well as local visitors. The Fête des Plantes Vivaces runs from 27-29 April (10am-6pm), admission €11. The Fête des Fruits et Legumes Oubliés runs from 10-12 November (10am-6pm), admission €11. Look out for the traditional buildings still used to storepotatoes, carrots, pumpkinsand other produce. The château at 91940 St-Jean-de-Beauregard is open Sundays (2-6pm) until the middle of Nov. Admission €8.50. Visit www.domsaint jeanbeauregard.com