Le Soleil va mourir (1977) by Christian Grenier, which would translate to "The Sun is dying" or "The Sun will die".
As far as I can see, there is no English translation. Most of the translations below are courtesy of DeepL.
Summary from Babelio:
2313: Pierre, Monica and Stefan live on giant Venus. Their mission? To make the planet habitable. When transgenic ferns grow there, the three scientists are overjoyed. Monica and Stefan, who love each other, return to Earth. Along the way, they send old and dangerous radioactive waste back to the Sun. Our star goes haywire. The verdict: the Sun will explode, and Earth will be swallowed up. But one thing is certain, Stefan and Monica's love will survive...
This extensive review hits most of the recollections, the only thing being misremembered is that the scientists were located on Venus, not Mars:
Monique and Stefan, recalled to Earth, come across radioactive debris lying around in space, put there by our 21st-century ancestors. Since this waste poses a danger to interplanetary navigation, the Earth base advises our two astronauts to take charge of cleaning up the mess. The decision was made to send the dangerous leftovers to the Sun, where they would be easily absorbed. No sooner said than done. On Earth, after a well-deserved rest, Monique and Stefan are called to Messigny, the planet's most famous astronomer.
Messigny is worried: he's noticed an upsurge in solar activity, which seems to be increasing again. After cross-checking his measurements with others, he has no doubt: the Sun has entered an explosive nova phase. Earth has three months to survive before the Sun explodes, wiping out the entire solar system. [...]
Given that it's not possible to move the Earth away from the Sun or protect it from the explosion, all that's left is to play on the relativity of time, so that the Earth lives in a relative time that's much slower than that of the cosmos, giving it enough time to find an emergency solution. Through the "Messigny Belt", a sufficient number of satellites generate a protective cocoon of relativistic particles around the globe, totally excluding it from the rest of the universe. Time on Earth now passes much more slowly; the three-month grace period becomes ten thousand years. [...]
However, Monique and Stefan could not accept that Pierre, who had remained on Venus, should be condemned. They convinced the town councillors that they were ready to look for him, thus condemning themselves to return to a land a thousand years older. Regarded as heroes, and with the onus on today's living to pass on their memory to future generations so that they can be properly welcomed back, our friends set off. They reach Pierre in extremis, but the rocket capsizes and goes down: it is no longer possible to leave the doomed planet. [...]
Suddenly, the convicts see some kind of extraordinary spacecraft, in the shape of a saucer, bearing down on them. They enter. [...] this craft was sent to their rescue by earthlings ten thousand years ahead of them (i.e. three months older by their standards), who had succeeded in moving the Earth towards the center of the galaxy, narrowly avoiding the end of their world.
Found with the Google query livre science fiction soleil champ temps site:babelio.com/livres (science fiction book sun field time site:babelio.com/livres). More precise queries, such as "temporal dilatation" or "red giant" would bring up the unrelated Tau Zero and The Wandering Earth.
