More than 50,000 people have signed an online petition in France demanding a replay of Tuesday's World Cup semi-final defeat to Spain, escalating a refereeing row that has followed Les Bleus out of the tournament and into the build-up to Sunday's final in New Jersey.

Spain won the semi-final 2-0 in Arlington, Texas, on 14 July. Mikel Oyarzabal opened the scoring from the penalty spot in the first half, and Pedro Porro added a second in the 58th minute to send La Roja through to face Argentina. It is that penalty, awarded by Salvadoran referee Iván Barton, that sits at the heart of the French grievance.

The sequence began with a loose ball in France's defensive third, where Lucas Digne swung at it and instead caught Lamine Yamal, prompting Barton to point to the spot. French supporters argue the passage of play should have been dead before the contact ever happened, because the ball had brushed Yamal's arm moments earlier. The petition puts it bluntly: during the penalty awarded to Spain, it states, Yamal touches the ball with his hand, France should not have conceded a first goal that changed the entire complexion of the match, and sport must be played by rules that, on the night, were not respected.

It is worth being precise about who is demanding what. The replay campaign is a fan-driven petition, not a formal challenge — the French Football Federation has lodged no protest or appeal with FIFA, and none is expected. World football's governing body has never granted a replay on the basis of a referee's judgement call, whose decisions on matters of fact are final under the laws of the game, and there is no procedural route by which a petition, however large, could overturn a completed semi-final.

The closest thing to an official French complaint came from the touchline. Didier Deschamps, whose final tournament as national coach ended with the defeat, pointedly asked reporters whether the referee was "up to the task of officiating a semi-final", adding that the penalty was not the only issue and that it "adds to everything else". His irritation also covered a 43rd-minute decision in which Barton awarded France a free-kick on the edge of the box for Fabián Ruiz's challenge on Ousmane Dembélé, then reversed his own call after consulting an assistant. Deschamps did, however, concede that his players' own errors had contributed to the loss.

FIFA's response was unequivocal. Pierluigi Collina, the governing body's director of refereeing and himself a World Cup final referee, was asked directly whether Barton had been up to the occasion. "Yes, absolutely," he said, insisting FIFA's referees are "world class" — and noting that the video assistant referee had reviewed the full penalty sequence during the match and supported the on-field award.

The technical case for the decision is also stronger than the petition allows. Under the current handball law, an offence requires the arm to make the body unnaturally bigger, and analysts who reviewed the footage noted that Yamal's arm stayed close to his side. Former FIFA-listed referee and broadcast rules analyst Christina Unkel observed that the contact came on the sleeve, which is not considered part of the arm for handball purposes.

There is an uncomfortable echo for France in the precedent, too. When Thierry Henry's unpunished handball set up the goal that denied the Republic of Ireland a place at the 2010 World Cup, FIFA flatly refused Irish requests for a replay. The same wall now stands in front of the French petition, whatever its signature count.

Spain, meanwhile, are preparing for Sunday's final against Argentina at MetLife Stadium, where Slovenia's Slavko Vinčić will become the first referee from his country to take charge of a World Cup final. The row over Arlington will rumble on in France, but the result — and Spain's place in the final — will stand.