IRAS 20319+3958 in Cygnus X South is a rare example of a free-floating globule (mass ~240 M<SUB>⊙</SUB>, length ~1.5 pc) with an internal H II region created by the stellar feedback of embedded intermediate-mass stars, in particular, one Herbig Be star. In Schneider et al. 2012, (A&A, 542, L18) and Djupvik et al. 2017, (A&A, 599, A37), we proposed that the emission of the far-infrared (FIR) lines of [C II] at 158 μm and [O I] at 145 μm in the globule head are mostly due to an internal photodissociation region (PDR). Here, we present a Herschel/HIFI [C II] 158 μm map of the whole globule and a large set of other FIR lines (mid-to high-J CO lines observed with Herschel/PACS and SPIRE, the [O I] 63 μm line and the <SUP>12</SUP>CO 16→15 line observed with upGREAT on SOFIA), covering the globule head and partly a position in the tail. The [C II] map revealed that the whole globule is probably rotating. Highly collimated, high-velocity [C II] emission is detected close to the Herbig Be star. We performed a PDR analysis using the KOSMA-τ PDR code for one position in the head and one in the tail. The observed FIR lines in the head can be reproduced with a two-component model: an extended, non-clumpy outer PDR shell and a clumpy, dense, and thin inner PDR layer, representing the interface between the H II region cavity and the external PDR. The modelled internal UV field of ~2500 G<SUB>°</SUB> is similar to what we obtained from the Herschel FIR fluxes, but lower than what we estimated from the census of the embedded stars. External illumination from the ~30 pc distant Cyg OB2 cluster, producing an UV field of ~150-600 G<SUB>°</SUB> as an upper limit, is responsible for most of the [C II] emission. For the tail, we modelled the emission with a non-clumpy component, exposed to a UV-field of around 140 G<SUB>°</SUB>. <P />The [C II] data shown in Figs. 4 and 5 (FITS files) are only available at the CDS via anonymous ftp to <A href="http://cdsarc.u-strasbg.fr">cdsarc.u-strasbg.fr</A> (ftp://130.79.128.5) or via <A href="http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/653/A108">http://cdsarc.u-strasbg.fr/viz-bin/cat/J/A+A/653/A108</A>Read less <