Vespucci and his voyages are sort of a mess.

We have two works supposedly written by him that were printed and widely circulated in the early 1500s, and three manuscript letters which were never printed and were found much later in a private collection traced to Medici family.

Of the two printed works first one is known as "Mundus Novus" or just "Letter to Lorenzo Medici from Lisbon", the other is known as "Four Voyages" or "Letter to Soderini". I will refer to them as Mundus Novus and "Four Voyages" and you can read them here The other three manuscript letters you can read in this work and I'll reference them as Manuscript letters.

The issue is that the "Four Voyages" work is almost certainly heavily made up on the basis of pre-existing accounts and the Manuscript letters which is why they contain some correct information. Similar doubt is brought about "Mundus Novus", even though it is describing a legitimate voyage, but it does have various serious inaccuracies in it. The modern writers share the opinion that the information in them is highly distorted, but is somewhat divided on the issue if "Four Voyages" and (with more doubt) "Mundus Novus" were compiled by third person (publishers of the letters for example) or by Vespucci himself.

One of the thing that falls immediately under scrutiny is the very existence of four voyages.

The supposed first voyage (described only in the "Four voyages") has probably never happened, especially not at dates it is written. We have documents placing Vespucci in Seville in the time of the first voyage, and we don't have records of any expedition in that period. And for the expedition to have taken place some time later is impossible due to the conflict it would be in with the "second" voyage of Vespucci (which is likely his actual first). Other issues with it are vague descriptions, implausible events (like talks with Indians on level that would be impossible with limited language familiarity) and other inaccuracies all confirming the belief this voyage is entirely made up.

The second voyage (first real one) is confirmed to have happened in 1499-1500, despite again inaccuracies of it in the Four Voyages description. But the first of the Manuscript letters (dated Seville 1500) also describes it in a much more convincing manner, and we have Spanish official documents corroborating it happened under captaincy of Alonso de Ojeda and that Vespucci was on it. The voyage made landfall on the north coast of South America and then explored areas to the south (apparently all the way to 6 degrees south of equator) and then north before going to Hispaniola and Bahamas and finally returning to Spain.

The third voyage (second real one) also certainly happened in 1501-1502, but unlike the previous one(s) that were conducted for Spanish, this one was for Portuguese, and it's function was to explore the coast of Brazil. The ships landed on the Brazllian coast and proceeded according to Vespucci in Manuscript letters to 50 degrees south (which might be little too much as it brings him almost.

The fourth voyage is also doubted to have had happened as we have little to no confirmation if it was real. It claims to be done for the Portuguese. The description in the unreliable "Four Voyages" is vague and tells that it was disastrous voyage with serious mishaps that accomplished little, only sailed down South America coast up to 18 degrees south and from there returned to Lisbon.

Overall, we can be certain in only two Vespucci voyages, both of which were exploring the continent of Southern America, and none going far up North. Here is one handy chart showing where they took place.

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So the answer to your question is: No, Vespucci did not reach Maine. The only voyage on which he would be remotely near it was the first one, for which 1) we have plenty of evidence it never happened 2) even if it did, it is very vague on how much north he arrived, and it's doubtful he reached all the way to Maine