I am trying to understand the Langer controversy. I have only have seen the Charedi side been explained. Are there any seforim/books/online articles which explain Rabbi Goren's position?
R. Goren wrote a 200 page book explaining his position (linked in Joel K's answer). If you're looking for something shorter and easier, R. J. David Bleich discussed this topic in the first volume of Contemporary Halachic Problems (p. 167 - 176). He summarizes R. Goren's five pronged argument as follows:
Rabbi Goren, claiming to have had additional evidence not available to the rabbinical courts which had previously held hearings on the matter, bases his decision on the following considerations:
There exists no admissible evidence attesting to Avraham Borokovsky's conversion to Judaism.
In the event that a valid conversion ceremony did take place, the conversion was nullified by virtue of the fact that Borokovsky continued to live as a practicing Christian. Rabbi Goren cites Zofnat Pa'aneah, (a commentary on the Mishneh Torah authored by the late Rabbi Yosef Rosen, in which Rabbi Rosen interprets Rambam as maintaining that subsequent idolatry on the part of a convert is tantamount to proof that the original conversion was insincere and hence invalid.
The original wedding ceremony between Chava Ginsberg and Avraham Borokovsky took place in a church. There is no evidence, argues Rabbi Goren, that they were subsequently married in accordance with the law of Israel.
The conversion of Avraham Borokovsky, if it indeed did take place, was the result of coercion on the part of Chava Ginsberg's father hence is null and void.
Even if the conversion were to be accepted as valid, Borokovsky, since he subsequently reverted to the practice of Christianity, would have the status of an apostate. Ba'al ha-Ma'or maintains that an apostate is not biblically qualified to issue a bill of divorce; according to Ba'al ha-Ma'or, a divorce executed by an apostate is valid only by virtue of rabbinic decree. It is, however, axiomatic that rabbinic legislation cannot validate a divorce which is biblically invalid. The formula invoked in such situations is an annulment of the original marriage. Such annulment is within the province of rabbinic jurisdiction, since all marriages are conducted according to "the law of Moses and Israel." The term "law of Moses" refers to biblical law, while "law of Israel" encompasses rabbinic legislation. Rabbi Goren argues that since Borokovsky is to be deemed an apostate, the bill of divorce which he ultimately delivered to Chava Langer had the effect of retroactively annulling their marriage. As a result, she was yet an "unwed woman" in the eyes of Jewish law at the time of her involvement with Otto Langer and hence the issue of that union are not to be considered bastards.
(This should not be taken to mean that R. Bleich supported R. Goren's position. Indeed, much of the rest of the article consists of counterpoints to these arguments.)
You can read Rav Goren’s own explanation of his pesak din here.