Emergency diplomatic visits are common occurrences when a major crisis arises or when two countries face a diplomatic emergency—it's all standard procedure.
Emily didn't even know how she got on the plane, only in a daze under the watchful eyes of countless people, she boarded the British diplomatic jet and arrived at the Paris airport in less than an hour.
Since it was an urgent visit, there had to be a reason, and this reason was too easy to find—a meeting between the two countries' intelligence systems over a major discovery was enough.
The information leaked by KGB was false, and both the UK and France denied it, sweeping this mess under the rug.
As for why Gao Yi was completely confident in his safety both before and after boarding the plane, the reason was simple—the British had a hundred thousand ways to kill him, but should he die, everything that had happened today would have come to light, leaving the British to consider only the hundred-thousand-and-first option.