“Him” is the sun. The line means that the “fair things” (the stars) that are “with” the sun now, are the same stars that were with the sun when the Divine Love (God) first moved them, that is, on the fourth day of creation (Genesis 1:14 “And God said, ‘Let there be lights in the expanse of the sky’”). Hence it is the same time of year as the creation.
From the perspective of a viewer on the Earth, the sun moves relative to the fixed stars along the path of the ecliptic, taking a year to complete the circuit. The region of sky near to the ecliptic is the zodiac and the stars in this region are divided into twelve signs: Aries, Taurus, Gemini and so on.
So Dante says that as he starts on his journey, the sun is with the same stars (in the same sign of the zodiac) as it was at the creation. Although the Bible does not specify a time of year for the creation, there was a medieval tradition that it took place at the spring equinox, for example:
Quo sane in loco primus seculi dies sit, nonnulli quaerentes, VIII Kalendarum Aprilium,† alii XII Kalendarum supradictarum die magis adnotandum putarunt, uno utrique, hoc est, aequinoctii argumento nitentes, quasi rationi congruat ut quia Deus aequis in principio partibus lucem tenebrasque diviserit, ibi praecipue tunc caput mundi, ubi nunc aequinoctium fieri credatur
Some have claimed that the first day of the world was the 8th kalends of April† [25 March], and others that it was the 12th [21 March]. In both cases they adduce the same argument, namely, the equinox. For it seems reasonable that because God in the beginning divided light and darkness into two equal parts, we should believe that the beginning of the world took place specifically at the point of the equinox.
Bede (725). De Temporum Ratione, chapter 6. In J. A. Giles, ed. (1843). The Complete Works of Venerable Bede, volume 6, pp. 153–154. London: Whittaker. Translated by Faith Wallis (1999). The Reckoning of Time, p. 24. Liverpool University Press.
† Bede means the eighth day before the kalends (the first) of April, since the Roman calendar counted downwards, and Roman counting was inclusive of both endpoints, so eight days brings us to 25th March.
(Strictly speaking, it’s not the case that the sun always rises with the same stars at the equinoxes, because the equinoxes slowly precess. The Earth’s axis precesses at about 50.3 seconds of arc per year, which would amount to more than 70 degrees in the roughly 5300 years from the traditional date of creation to the start of the Inferno. Medieval astrologers and calendarians treated the zodiacal signs as fixed to the spring equinox, so that the signs gradually drifted from the constellations that they were originally associated with.)
Putting this together, the passage quoted in the question locates the start of the Divine Comedy in spring, the “sweet season” of new life and “good hope”, symbolising the poet’s sprirtual rebirth. Later in the poem there is a more precise time reference:
In just five hours it will be, since the bridge fell,
a thousand two hundred sixty-six years and a day;
that was the time the big quake shook all Hell.
Dante (1314). Inferno 21.112–114. Translated by John Ciardi (1954). New American Library.
The “big quake” was caused by Christ entering Hell and breaking its gates, after his death on Good Friday in the year AD 34. By working backwards from canto 21 we find that the opening of the poem takes place on Good Friday (8th April) in the year 1300.
(Again, strictly speaking, this isn’t quite right, because 8th April 34 was a Saturday. But it seems clear that it is the anniversary of Good Friday that is meant, and in any case, Malacoda, the speaker in Inferno canto 21, is a demon, not a calendarian.)