Primarily an aeronautical company, Matra first became involved in sports cars in 1964. Later they graduated to Formula One with some impressive results. In 1970 they began a partnership with Simca. This allowed them to sell their then current sportscar, the M530, in Simca dealers across Europe. The benefit to Simca was seeing their name on a series of Le Mans winning cars in the early 1970s, and also the opportunity for their mechanical components to be used in subsequent Matra sportscars. The M530 had a Ford engine, and Chrysler were understandably not that enthusiastic about it being sold in Simca dealers.

Matra unveiled the successor to the M530, the M550, in spring 1973. Although coded 550, the car had a name, Bagheera, after the panther in "The Jungle Book". Like the 530, it was mid engined. But it was a much sleeker machine, incorporating three abreast seats, and a rear hatch, which gave access to the top of the engine compartment behind the driver's and passengers' heads. The engine was the 1294 cc unit found in the Simca 1100 TI, tuned by Matra's engineers to produce 84 bhp, with a top speed of around 101mph. The chassis was tubular incorporating a roll over structure. To this was bonded the plastics body. The car was both extremely aerodynamically efficient and immensely strong. Unfortunately, Matra had not given as much thought as they should to allowing water to drain off the metal structure, with the result, over time, that the steel framework rusted underneath the smart looking bodywork. Both the torsion bar suspension and the four speed gearbox were also taken from the Simca 1100.

With very few native sportscars in France, the Bagheera was an immediate success, although Matra's limited production facilities would prevent it from ever being a common sight. British motoring journalists who drove Bagheeras in France loved the car, but doubted that it would ever be sold in the UK. L J K Setright described it as " the closest car yet to a baby Lamborghini Urraco". In July 1975 a new model, the Bagheera S was introduced, which used a 90 bhp version of the Simca 1308 1442cc engine. Top speed went up to 109 mph.

One year later an extensively revised Bagheera arrived on the scene. The body had been restyled to give a longer bonnet, wrap-around bumpers, new rear lights and new interiors. Only the rear hatch was carried over unchanged from the earlier car. The mechanical components remained as before. In August 1977 it was announced in the UK that one of the Bagheeras, the S, was to be officially imported by Chrysler, but in left hand drive format only. The price was £5,370, a massive sum in 1977. An enterprising Chrysler dealer, Walchry Motors of Walton-on-Thames, Surrey, commissioned a local firm, Hodec of Old Woking, to convert a batch of these UK Bagheeras to right hand drive, which added a further £625 to the price. Despite the high price, the cars found willing buyers in the UK. Back in France, a new model was launched, the Bagheera X. This was originally supplied either in green or black, with contrasting bold graphics on the lower bodywork and side bumpers, plus a velour interior. Fitted with the 1442 cc engine, it was mechanically identical to the S.

In October 1978, Chrysler UK announced that the Bagheera S would only be available in right hand drive format, with a folding sunroof was fitted as standard. All Bagheeras were fitted with a new dashboard, and the 1294 cc engine in the base model Bagheera was replaced with the 1442 cc unit. The advent of the revived Talbot marque in place of Chrysler in Europe in July 1979 saw the names of the cars change from Matra-Simca to Talbot Matra. UK imports stopped, and the Bagheera S was discontinued. For the first time, the doors were given conventional handles instead of the Renault 5 type arrangement of recesses to put your fingers behind in order to open the door. Production of the Bagheera finished in mid 1980 after 47,802 cars had been built.