  Background: Odd-odd nuclei, around doubly closed shells, have been
extensively used to study proton-neutron interactions. However, the evolution
of these interactions as a function of the binding energy, ultimately when
nuclei become unbound, is poorly known. The $^{26}$F nucleus, composed of a
deeply bound $\pi0d\_{5/2}$ proton and an unbound $\nu0d\_{3/2}$ neutron on top
of an $^{24}$O core, is particularly adapted for this purpose. The coupling of
this proton and neutron results in a $J^{\pi} = 1^{+}\_1 - 4^{+}\_1$ multiplet,
whose energies must be determined to study the influence of the proximity of
the continuum on the corresponding proton-neutron interaction. The $J^{\pi} =
1^{+}\_1, 2^{+}\_1,4^{+}\_1$ bound states have been determined, and only a
clear identification of the $J^{\pi} =3^{+}\_1$ is missing.Purpose: We wish to
complete the study of the $J^{\pi} = 1^{+}\_1 - 4^{+}\_1$ multiplet in
$^{26}$F, by studying the energy and width of the $J^{\pi} =3^{+}\_1$ unbound
state. The method was firstly validated by the study of unbound states in
$^{25}$F, for which resonances were already observed in a previous
experiment.Method: Radioactive beams of $^{26}$Ne and $^{27}$Ne, produced at
about $440A$\,MeV by the FRagment Separator at the GSI facility, were used to
populate unbound states in $^{25}$F and $^{26}$F via one-proton knockout
reactions on a CH$\_2$ target, located at the object focal point of the
R$^3$B/LAND setup. The detection of emitted $\gamma$-rays and neutrons, added
to the reconstruction of the momentum vector of the $A-1$ nuclei, allowed the
determination of the energy of three unbound states in $^{25}$F and two in
$^{26}$F. Results: Based on its width and decay properties, the first unbound
state in $^{25}$F is proposed to be a $J^{\pi} = 1/2^-$ arising from a
$p\_{1/2}$ proton-hole state. In $^{26}$F, the first resonance at 323(33)~keV
is proposed to be the $J^{\pi} =3^{+}\_1$ member of the $J^{\pi} = 1^{+}\_1 -
4^{+}\_1$ multiplet. Energies of observed states in $^{25,26}$F have been
compared to calculations using the independent-particle shell model, a
phenomenological shell-model, and the ab initio valence-space in-medium
similarity renormalization group method.Conclusions: The deduced effective
proton-neutron interaction is weakened by about 30-40\% in comparison to the
models, pointing to the need of implementing the role of the continuum in
theoretical descriptions, or to a wrong determination of the atomic mass of
$^{26}$F.
