This sounds very much like Alastair Reynold’s
Century Rain (2004).
Wikipedia
: “Wendell Floyd is an expatriate American living in an
alternate version of 1950s
Paris. In this world, the
Naziinvasion of France failed, and
Hitler was deposed by
the German High Command. Without
World War II, technology in this world has stagnated at 1930s levels, and
Fascist political parties have gained power in
France.
Floyd is a part-time
jazz musician whose career has stalled since his ex-girlfriend, Greta, left Paris to pursue a musical career touring with another jazz band. He and his band-mate André Custine earn a supplemental income working as
private detectives…
In a scene seemingly from another novel, Verity Auger finds herself responsible when her
archaeology dig beneath the frozen ruins of some far-flung future Paris results in the death of one of her students. During her trial she is caught up in political infighting, and maneuvered into accepting a high risk assignment, without knowing what it entails.
Things get even more bizarre when she finds out that at the other end of the portal is an alternate-history version of Earth in the year 1959 – almost 300 years behind her present-day – and that she is to retrieve a tin of documents that was left behind by Susan White, an earlier agent sent to "Earth Two", who died under mysterious circumstances.”
en.m.wikipedia.org