What "time travel" story required the traveller to mentally reconstruct his world in order to return to it?
"Flux" by Michael Moorcock and Barrington J. Bayley, first published in New Worlds Science Fiction #132, July 1963, available at the Internet Archive.
1. The protagonist is sent a relatively short distance into the future (maybe a year? I've forgotten).
"Our only hope lies in discovering how events are organized in time—this might sound highly speculative for such a serious and practical matter, but this is what things have come to. In order to take effective action in the present, we must know the future. This is the mission we have in mind for you. The Research Complex at Geneva has found a way to deposit a man some years in the future and bring him back. You will be sent ten years forward to find out what will happen and how it will come about. You will then return, report your findings to us, and we will use this information to guide our actions, and also—scientifically—to analyze the laws governing the sequence of time. This is how we hope to formulate a method of human government for use by future ages, and, perhaps, remove the random element from human affairs."
2. When he arrives in this "future" he finds himself in a completely different world, with non-human inhabitants.
A group of bipeds was advancing, straggling on bony, delicate limbs through knee-deep strata of purple clouds which rolled in masses a few hundred yards away. They were humanoid, but skeletal, ugly, and clearly not human. The leader, who was over seven feet tall, was shouting and pointing at File and the machine.
Another waved his hands: "Sa Skrrak—dek svala yaal!"
3. The inhabitants use a machine to teach him their torturous language.
In the course of the meal, File also discovered that the machine the warrior had trained on him in the desert was 100 percent efficient. He had been completely reeducated to talk and think in another language, even though he could, if he chose, detach himself slightly, hear the strangeness of the sounds which came from both his mouth and those of the Yulk.
4. He tries to return home, and (eventually) finds himself in a realm of chaos/nothingness.
The formless universe around him began to vanish as he went to an immense distance and beyond the limits of speed. Matter was breaking up, disappearing. Still he rushed on in terror, until the time machine fell away beneath him, and the matter of his body disintegrated and vanished.
He was a bodiless intelligence, hurtling through the void. Then his emotions began to vanish. His thoughts. His identity. The sensation of movement dropped away. Max File was gone. Nothing to see, hear, feel, or know.
5. He laboriously reconstructs in his mind everything he can remember about his home and finds himself back there somehow.
It was a newfound delight. He could make anything! For ages he experimented, creating everything he could think of. Once, a whole world formed beneath him, complete with civilizations, a tiny sun, and rocket-ships reaching out.
He canceled it at once. It was enough to know that his every intention, even his vaguest and grandest thought, was translated into detail.
Now he had a means to return home—and now he could solve the government's problem for good and all.
For if he could not find Europe, could he not create it over again? Would that not be just as good? In fact, it was a point of philosophy whether it would not be in fact the same Europe. This was Nietzsche's belief, he remembered—his hope of personal immortality. Since, in the boundless universe, he was bound to recur—File's discoveries had reinforced this view, anyhow—he could not die. Two identical objects shared the same existence.
6. The twist is
that in his "home" reality everyone speaks the language he was taught by the non-human inhabitants at his first stop.
"You're back on the dot, old man! As a test flight it was perfect—from our end." He flicked his finger over his shoulder. "Bring brandy for the man! You look done in, Max. Come and clean up; then you can tell us how it went . . ."
File nodded, smiling wordlessly. It was almost perfect . . . but he had not realized just how efficiently he had been taught a new language.
Appeltoft had spoken to him in the voice-torturing tongue of the Yulk.