It's possible if UK and France resisted the decision to unite two parts of Germany. IRL they there opposed to the idea of united Germany and it took some persuasive talks and joint US/USSR statement to enforce the decision.
They still were WWII victorious countries, you know. They have a right to oppose the unification.
Before the fall of the Berlin Wall, British Prime Minister Margaret Thatcher told Soviet President Mikhail Gorbachev that neither the United Kingdom nor Western Europe wanted the reunification of Germany. Thatcher also clarified she wanted the Soviet leader to do what he could to stop it, telling Gorbachev "We do not want a united Germany".
Although she welcomed East German democracy, Thatcher worried that a rapid reunification might weaken Gorbachev, and favoured Soviet troops staying in East Germany as long as possible to act as a counterweight to a united Germany.
“ We defeated the Germans twice! And now they're back! ”
— Margaret Thatcher, December 1989
Thatcher, who carried in her handbag a map of Germany's 1937 borders to show others the "German problem", feared that its "national character", size and central location in Europe would cause the nation to be a "destabilizing rather than a stabilizing force in Europe".
So it was entirely possible these two states to co-exist until modern days. With leaky borders, maybe in some form of confederacy, but still formally divided. Like Russia and Belarus. Like Serbia and Montenegro. Like Czech Republic and Slovakia.