The pressure was on after Sweden had earlier swept past Luxembourg 8-0 to boost their hopes of making it to Russia, which in turn all but eliminated Holland, who later won 3-1 in Belarus.
Juventus midfielder Matuidi lashed home an angled finish after just three minutes in Sofia, which leaves Les Bleus a point clear of Sweden and crucially with fate in their own hands ahead of the visit of Belarus on Tuesday.
Earlier on Saturday, Sweden thrashed Luxembourg in Solna, which temporarily put them ahead of France at the top of the group.
Al Ain striker Marcus Berg netted four goals and captain Andreas Granqvist scored a penalty in each half as the Swedes recorded their biggest victory since 1938.
Luxembourg's worst defeat in 35 years put them bottom of the group, now with a goal difference of minus 18.
Despite Holland's victory at the Borisov Arena, the Dutch look set to miss out on another major tournament given their inferior goal difference.
Dick Advocaat's side will host Sweden in Amsterdam with the visitors' goal difference now some 12 better after their resounding victory over Luxembourg.
Brighton midfielder Davy Propper put the Oranje ahead against Belarus on 24 minutes, but defender Maksim Valadzko levelled 10 minutes into the second half.
With time running out, Holland took the lead again through a penalty from Arjen Robben on 84 minutes before Memphis Depay made it 3-1 with a free-kick in stoppage time.