Singularity has always been ingrained in the Coupe de France and this season is no exception. The centenary final, to be held on Tuesday, pits Paris Saint-Germain against Les Herbiers, who hail from a small town in western France of 16,000 people and have an average attendance of 1,400.

In financial terms, too, there is no contest: PSG’s budget is 275 times that of Les Herbiers (around £1.7m), who turned professional only three years ago and play in the third tier of French football, where they sit just above the relegation zone. Their squad, mostly made up of free transfers and a few loanees (with three players having briefly experienced Ligue 1), has cost nothing to assemble and the average monthly wage is £2,200.

But one secret weapon the rich Parisians may envy the club from the Vendée region for is their No 1 supporter Philippe Katerine, a local who is France’s most eccentric singer, thanks notably to his madcap hit Louxor J’adore, the offbeat clip of which was shot in a village near Les Herbiers. The humorous provocateur, famed for his surrealist and irreverent lyrics, has released a trademark unconventional cup final anthem, an odd call to arms titled 85 rouge et noir.

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In the semi-final, the Vendéens eliminated another small third-tier club, Chambly, who have racked up 11 promotions since their inception in 1989 in the 14th division, a feat achieved without benefiting from the largesse of a wealthy benefactor. Chambly, modelled on a defensive Internazionale by the French-Italian Luzi family which has run the club for the last three decades, had dispatched Ligue 1 Strasbourg in the quarter-finals but were no match for Les Herbiers’s all-attacking style. Sadly, the founder of the club, Walter Luzi, died on the day of the semi-final, played at Nantes’s La Beaujoire stadium in front of a capacity crowd of 35,000. Last season in the last 32, Chambly had held Monaco to a pulsating 3-3 draw in normal time before losing 5-4 in extra time

Les Herbiers’ captain, Sébastien Flochon, rates his team’s chances of beating PSG at the Stade de France at “about 0.5%” but as L’Équipe printed on its front page of 18 April, the proud Vendée, which revolted en masse against government troops during the French revolution, is in heaven. Not least because their cup odyssey has boosted the club’s coffers by £1.6m, with a £650,000 bonus on offer to the winner.

Although no team below the second tier have won the trophy (second division Le Havre and Guingamp achieved this in 1959 and 2009, respectively), giantkillers – les tombeurs de gros – such as Chambly hold a special place in Coupe de France lore. Calais shot to national prominence in 2000 when, as a fourth division side, they reached the final. “Calaismania” swept the country and they lost 2-1 to Nantes only because of a dubious stoppage-time penalty.

Similar exploits are fairly commonplace in the Coupe. The first petit poucet (minnows) were arguably the Algerian amateurs of El Biar who, in 1957, knocked out two second-tier clubs before defeating Reims, the European Cup runners-up the year before, 2-0 in the last 32. In 1996 and 2001 third division Nîmes and Amiens toppled five top-flight clubs between them on their way to the final. In 2012 third division Quevilly battled to the final, where they fell 1-0 to Lyon after putting out Ligue 1 Marseille and Rennes. Quevilly are no strangers to “cupsets”: most notably, in 1927, they lost to Marseille in the final.

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Over the past five years alone 15 amateur or semi-professional clubs (fourth division and below) have reached the last 16. The difference in level between the top three divisions and the rest is relatively small in France and the gradual introduction of a series of rules designed to protect teams in the lower leagues, such as home advantage, perhaps explains the phenomenon. The absence of replays also favours underdogs who, over time, have grown in confidence.

French cinema consecrated plucky minnows in the 1979 box-office hit Coup de Tête, a satirical comedy centred around the fictitious AS Trincamp. The film was inspired by the rise of Auxerre and Guingamp’s heroic cup feats of 1973 when the then fifth division team beat four second division clubs. Guingamp used the cup proceeds (£90,000) to mount several promotion campaigns that took them to the top flight in 1995, where they have largely remained, an astonishing achievement for a town the size of Totnes.

The Coupe de France was founded in 1917 on the initiative of Henri Delaunay, chairman of the forerunner of the French Football Federation, who was impressed by the vibrancy of the FA Cup. Delaunay felt the Coupe could play a unifying role in a country torn asunder by the first world war and decreed that it should be open to all French clubs, irrespective of level. More than 8,000 teams enter each year, including hundreds in the French overseas territories, and the tournament kicks off with regional rounds some 13 months before the final in May the following year, making it the most inclusive and largest domestic competition in world football.

The 11 best overseas clubs – les ultramarins – enter at the seventh round in November (there are 14 rounds; 15 in the larger regions) along with Ligue 2 clubs. The FFF covers expenses for clubs drawn to play in mainland France or overseas. As round-trip distances can exceed 20,000 miles, clubs usually make a mini holiday of it.

However, for the first time in four years no ultramarin got past the preliminary rounds and, although this may be a blip, it could also reflect the parlous financial state of French overseas football. Many clubs are in effect bankrupt and the FFF is increasingly having to bail out local leagues as they struggle to retain promising players keen to relocate to mainland France for football or professional reasons.

Exceptionally, for various reasons, the final will be played on a Tuesday – a bank holiday. That may take a few fans by surprise but this mismatch between PSG and Vendée Les Herbiers is unlikely to deter lovers of the rebellious and unpredictable spirit of the Coupe de France: the most watched Coupe final of the past decade is Lyon v third-tier Quevilly in 2012 with nearly seven million viewers, twice as many as last year’s final between PSG and Angers.

Kevin Quigagne is a former football writer for Les Cahiers du football