Paris-based Peugeot led the fall, with an 18 percent drop in registrations that eroded its market share to 11 percent for the first eight months, down almost a percentage point year-on-year.
Italy's Fiat dropped 4.9 percent, in line with overall demand. Market leader Volkswagen fell 11 percent, weighed down by declining sales at its namesake brand.
VW's German luxury peers have increased their sales, partly at the expense of European volume brands.
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BMW registrations jumped 9.9 percent in August and were little changed for the first eight months, lifting the group's market share for the period.
That compared with a 0.5 percentage point gain for Daimler, powered by Mercedes-Benz sales that rose 8.5 percent in August and 5.5 percent for the year so far.
VW's Audi, the weakest European performer of the three German premiums, still increased share in January-August with a 3.6 percent dip in sales, less than the market decline. August registrations were down 6.4 percent.
Renault also bucked the trend with a 5.8 percent gain in August and a modest 2.2 percent decline for the first eight months, saved by strong sales of its Dacia no-frills cars.
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South Korea's Hyundai and affiliate Kia, whose combined deliveries fell 4.7 percent last month, have also won business from their European mass-market rivals.
"What we're seeing right now in the European car industry is a squeezed middle," Hyundai Europe chief Allan Rushforth said in an emailed statement.
"German premium brands are coming down through the market while Hyundai is moving up (and) making life very difficult for European volume brands rooted in the mainstream."
Hyundai-Kia limited their sales decline this year to 1.3 percent, resisting the worst of the slump.
Renault's Japanese affiliate Nissan and the Toyota brand also declined by less than the broader market.