What if he touched the wine and then repented?

Then there is no question at all. Why should the wine become forbidden? Ordinary gentile wine is not an intrinsic object-based prohibition. Now its owner is a kosher Jew.
In any case, there is no prohibition on a person’s own wine.

With God's help, 15 Shevat 5784

In my comment (under the screen name: "Sabbath Desecrator") on Column 471, I noted, among other things, Rabbi Shmuel Baruch Ganot’s responsum (on the "Din" website) regarding permission for the Sabbath desecrator himself to drink wine that he touched. He cited Rabbi Moshe Feinstein’s view, who permitted it on the grounds that a person is not required to distance himself from himself, and Rabbi Yosef Klopft’s view, who prohibited it because of "no distinction was made." I also cited Rabbi A. N. Z. Roth, who ruled leniently for the Jewish hospital in Budapest to serve wine to a Sabbath desecrator, for the same reason—that he is not required to distance himself from himself.

Best regards, Fish"l

What do you mean by "now its owner is a kosher Jew"? A Jew who buys wine from a gentile is still forbidden to drink the wine even though now the owner is a kosher Jew.

🙂 The original owner is now kosher. The current owner obviously makes no difference with regard to the prohibition.

So if a gentile sold wine to a Jew and then converted, does the wine become permitted?

I understand that your reasoning regarding one’s own wine is like what Fish"l brought here in the name of Rabbi Moshe Feinstein—that a person is not required to distance himself from himself. And that is understandable reasoning when he is still "holding the creeping thing in his hand," where there is no point in immersing. But after he repented and his heart was transformed into that of another person, then seemingly there is certainly room for the reasoning that he must distance himself from who he was in the past—even more so than his obligation to distance himself from the wine of other apostates (who already sold the wine, or died, or repented).

That is open to discussion, mainly because of "no distinction was made," and because libation wine, unlike ordinary gentile wine, is an intrinsic object-based prohibition, and once the prohibition takes effect there is room to argue that it does not simply lapse on its own.
As for oneself, that seems obvious to me.
And the pilpul about distancing oneself from one’s former self may be nice for the laws of repentance ("I am not that same man"…), but not for practical Jewish law.

Do you mean that ordinary gentile wine is prohibited because of concern over intermarriage, and not because of concern that it may have been used for libation?
Maybe one could look for proof in Avodah Zarah 57: if someone circumcised but did not immerse, his wine is libation wine (as is the law for ordinary gentile wine)—would anyone say there that after he completes the immersion the wine becomes permitted again? And one should check the law regarding a gentile holding wine who converted—may he sell it to a Jew?

[I don’t understand why this is so obvious to you, and it doesn’t seem like pilpul to me. More generally, my tendency is that a person regards himself exactly as he regards anyone else. So when, for example, he considers whether morality obligates him to do some act that will also cause him suffering, his duty is to weigh the moral obligation not to cause suffering to himself exactly as morality forbids him to cause suffering to others. And if I understood correctly what you informed me in the past, you think morality does not forbid a person to hurt himself against his own will. And in my view too, a person’s own opinion is no more important than another’s opinion in a place where he himself admits that his opinion is probably mistaken—and not like "self-authorization" in Jewish law.]

Indeed. In my opinion, formal substitutions of a general variable with the person himself do not work well in Jewish law. The pilpulim are well known about someone who threw a vessel from the roof and he himself then ran and caught it on the edge, and likewise about setting one’s own dog on someone.
This is connected to Atvan DeOraita on one who rounds his own hair (there was a column about that), and also to the column on Shalom Hanoch’s song "A person dwells within himself as a stranger."

I wrote with those columns in mind, and while accepting that they are correct (except for a few details that I argued about there and elsewhere when the issue came up).