At the vast Rungis food market outside the French capital, wholesale fruit and vegetable companies were feeling the effect of French farmer protests, as tractors and hay-bales blocked motorways in what some demonstrators have called the “Siege of Paris”. “Merchandise hasn’t arrived, there’s definitely an impact,” said Célia, who works at a wholesale fruit and vegetable firm with 12 staff, supplying shops and restaurants in the city. “It’s carrots, potatoes, cabbages, all kinds of fruit and vegetables. Deliveries are very difficult because of the roadblocks. Around 40% of our vegetables haven’t been delivered today and it has been difficult since yesterday for both French and European produce. Everyone is affected and it will continue like that for the coming days.” French police warned that about 1,000 farmers and 500 tractors were barricading roads across France, and the protests could intensify this week over farmers’ demands for better prices for their produce and more government support. The new prime minister, Gabriel Attal, told parliament on Tuesday that French farming is “our strength and pride”. He promised France would work to extend an exemption on EU fallow land rules and Paris would set up an emergency fund for struggling wine producers alongside other help for farmers. But the farming crisis looked likely to continue all week. Teachers and school support staff were to strike across France on Thursday amid calls for better pay and recruitment. Some farmers on the motorway barricades have spoken of “starving out Paris” in order to get government action on low prices for products, to cut red-tape, and, they argued, to “save the rural way of life”. But Arnaud Rousseau, the leader of the biggest farmers’ union, the FNSEA, said he was against any disruption of food distribution. “Our objective is not to starve French people, but to feed them,” he told the Europe 1 broadcaster. About 200 southern farmers were on a tractor go-slow snaking through the country and hoping to reach Rungis – Europe’s largest fresh food market – but they had paused in central France on Tuesday morning after police diverted them. The government and French police are seeking to stop any protests from reaching the vast food delivery bays of Rungis, south east of Paris. But the fact that hundreds more farmers and tractors continued to block key motorways on the outskirts of Paris and across France this week was already having an impact on food deliveries. Amid massive public support for the farmers, concern is growing that if road blockades intensify, it could cause difficulties in the food supply chain this week. Bakeries across France have been sending free croissants and baguettes to the barricades to support the farmers, but many are concerned that if motorway blockades continue long-term, it could have an impact on lorries delivering flour and ingredients that would affect businesses making bread, sandwiches, cakes and pâtisserie. Dominique Anract, a baker in western Paris, is president of the French confederation of Boulangerie and Pâtisserie as well as the European Federation of Bakers and the International Union of Bakers. He said: “There are two ways this could really affect us. First, supply. In big cities, bakeries don’t have much space to store ingredients. Perishables – milk, eggs, cream – cannot be stored for long. So without deliveries of items such as flour for bread, or fruit and vegetables for tarts, we would be in difficulty. Artisan bakers use French flour. Most bakers take flour deliveries every week, some every day, and so that’s very worrying. Also, every time there are strikes or protest movements like this, lots of people work from home because they can’t travel to work, so bakery snacks and sandwiches see a big drop in sales. There would be an impact on takings.” Anract said bakers supported the farmers “because they are our suppliers and we pay them well, we pay a good price for their products … they supply us, they feed France.” But he said at some point, the government must find solutions for the crisis, which would imply discussions at EU level, and would take time. There were 40km (25 miles) of traffic jams around Paris by late morning on Tuesday, as commuters were advised to carefully plan routes to avoid farmers who had shut key motorways. From her desk at small family-run transport company south-east of Paris, Tiffany was continuing to process orders for lorry deliveries and collections despite several hay-bale blockades outside Paris. “We support the farmers’ blockades and their protest movement but we’ve got to keep working, we’ve got to keep the country going,” she said. The company’s four staff lived nearby and had been able to get into work and keep driving lorries. A key issue this week is policing. Whereas protests by environmental protesters in recent months have seen an immediate response by riot police to dislodge them, the farmers have been allowed to stay on motorway barricades as police monitor the situation. The interior minister, Gérald Darmanin, has said he did not want to respond to farmers’ “suffering” by sending in riot police. A test will be the police blocks stationed around Rungis and whether farmers attempt to reach the market this week.