We study the topology of the 3D magnetic field in a filament channel to address the following questions: Is a filament always formed in a single flux tube? How does the photospheric magnetic field lead to filament interruptions and to feet formation? What is the relation between feet-related field lines and the parasitic polarities? What can topological analyses teach us about EUV filament channels? To do so, we consider a filament observed on 6 October 2004 with THEMIS/MTR, in Hα with the full line profile simultaneously and cospatially with its photospheric vector magnetic field. The coronal magnetic field was calculated from a “linear magnetohydrostatic” extrapolation of a composite THEMIS-MDI magnetogram. Its free parameters were adjusted to get the best match possible between the distribution of modeled plasma-supporting dips and the Hα filament morphology. The model results in moderate plasma β≤1 at low altitudes in the filament, in conjunction with non-negligible departures from force-freeness measured by various metrics. The filament here is formed by a split flux tube. One part of the flux tube is rooted in the photosphere aside an observed interruption in the filament. This splitted topology is due to strong network polarities on the edge of the filament channel, not to flux concentrations closer to the filament. We focus our study to the northwest portion of the filament. The related flux tube is highly fragmented at low altitudes. This fragmentation is due to small flux concentrations of two types. First, some locally distort the tube, leading to noticeable thickness variations along the filament body. Second, parasitic polarities, associated with filament feet, result in secondary dips above the related local inversion line. These dips belong to long field lines that pass below the flux tube. Many of these field lines are not rooted near the related foot. Finally, the present model shows that the coronal void interpretation cannot be ruled out to interpret the wideness of EUV filament channels.