The rule for a creature's size is as follows on Monster Manual page 6:
$$
\begin{array}{lll}
\textbf{Size} & \textbf{Space} & \textbf{Examples} \\
\hline
\text{Tiny} & \text{2½ by 2½ ft.} & \text{Imp, sprite} \\
\text{Small} & \text{5 by 5 ft.} & \text{Giant rat, goblin} \\
\text{Medium} & \text{5 by 5 ft.} & \text{Orc, werewolf} \\
\text{Large} & \text{10 by 10 ft.} & \text{Hippogriff, ogre} \\
\text{Huge} & \text{15 by 15 ft.} & \text{Fire giant, treant} \\
\text{Gargantuan} & \text{20 by 20 ft. or larger} & \text{Kraken, purple worm} \\
\end{array}
$$
The Monster Manual page 268 states:
A scaly biped, the tarrasque is fifty feet tall and
seventy feet long, weighing hundreds of tons.
And the Reduce use of the Enlarge/Reduce spell states:
The target's size is halved in all dimensions, and its weight is reduced to one-eighth of normal. This reduction decreases its size by one category – from Medium to Small, for example.
Emphasis mine.
In the case of our Tarrasque, these statements in Reduce are contradictory. Its new size is now 25′×35′, which means it's still classified as Gargantuan.
Which rule takes priority?
We can break the rules even more here. If we assume the Tarrasque is now huge rather than gargantuan, PHB 192 states:
Squeezing into a Smaller Space: A creature can squeeze through a space that is large enough for a creature one size smaller than it. Thus, a Large creature can squeeze through a passage that's only 5 feet wide. While squeezing through a space, a creature must spend 1 extra foot for every foot it moves there, and it has disadvantage on attack rolls and Dexterity saving throws. Attack rolls against the creature have advantage while it’s in the smaller space.
This means our 25′×35′ beastie can now get through a 10 foot door.
Best Answer
This is one of those edge cases where a DM would need to make a ruling.
Given that the Tarrasque is exceptionally large, it would be reasonable for the line
to take precedence over the line
In other word, the Tarrasque is reduced by more than half such that it can be considered a Huge creature, rather than still a Gargantuan creature. Given that magic has been used to reduce the Tarrasque (meaning that presumably a resource has been expended and the Tarrasque has failed a save, etc), it seems fair for the Tarrasque's opponents (presumably the party) that this should be the case.
Of course, it may also be reasonable for a DM to say that the Tarrasque is so large that reducing doesn't reduce its category, so the lines above take precedence the other way around, leaving the reduced Tarrasque as still being a Gargantuan creature.
Ultimately, without a Word of God answer, this one is up to the DM.