Sweden, second in the group, hold a three-point lead and a goal difference that is better by 12 goals over the Dutch, who they meet on Tuesday.
The Dutch won 3-1 in Belarus, while France beat Bulgaria 1-0 to maintain their one-point lead over Sweden.
France will qualify as group winners if they beat Belarus on Tuesday.
Sweden can take advantage if France drop points, otherwise they are likely to have to settle for a place in the play-offs.
Marcus Berg scored four times for Sweden as Luxembourg, who drew 0-0 with France in September, were embarrassed.
The Netherlands, runners-up in 2010 and third in 2014, also failed to qualify for the 2016 European Championships.
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