Indeed a line does not consist of a denumerable ordering of points, but of a non-denumerable ordering of points. In this latter way a line does consist of points.
The mathematical subdiscipline Point Set Topology ( = the topology of point sets) treats of this problem (of continuity). Philosophically, however, all this remains problematic : The line is a (mathematical) continuum, and in such a continuum its parts are only potential(ly) there : The continuum is divisible (and on actual and continued division of it it results in a potentially infinite number of points, and thus always results in a finite number of points), but not divided. The points that are obtained on actually dividing the continuum (the line) can be viewed, not as the parts of the line, but as boundaries between (possible) parts.