I am widowed and know little of my Jewish Heritage. Of this, I know, I observe the Torah and do my best to abide by it. Since I know little, and I am interested in marrying a non-Jew who is a Free Mason, will that be a contradictory?
I can see that your Jewish Heritage is important to you. I recommend that as you try to learn more about Judaism, you visit the Aish HaTorah website - http://www.aish.com/ - which has a great deal of information that would likely interest you about Judaism.
On the topic of intermarriage, in the Torah (D'varim 7:3), God commands the Jewish people:
"And you shall not intermarry with them; do not give your daughter to his son, and do not take his daughter for your son."
It is from this source that we learn that interfaith marital relationships are prohibited (Maimonides, Hil. Issurei Bi'ah, 12:1; Shulchan Aruch, EH 16:1). Furthermore, intermarriage is not recognized (Shulchan Aruch, EH 44:8).
I recommend that you ask the Rabbi anything you would like on the website by visiting this link on Aish HaTorah's website and then clicking on "Ask the Aish Rabbi a Question."
Since you say that your friend is not Jewish, the above answer by Toras Emes 613 applies. But since the question itself raises the question that Freemasons themselves are not kosher, I write as follows: As long as the Freemason is a Jew, and one is otherwise eligible to marry him (e.g. not closely-related, or a divorcee and the man is a kohen), there is no reason why a Jewish woman cannot marry a Mason. Freemasonry is not a religion. See United Grand Lodge FAQs. It is a fraternal organization which takes members from all religions, including Judaism. The organization requires that its members believe in a supreme being, but do not specify how. Members of my Orthodox synagogue are Freemasons and I attended a funeral conducted by Rabbi Kalman Winter, zt'l, which included Freemason ceremonies in addition to standard Orthodox Jewish funeral practices. Furthermore, I asked Rabbi Gedaliah Anemer, zt'l, Rosh HaYeshiva of the Yeshiva of Greater Washington, whether there was any prohibition to a Jew becoming a Mason, and he said that from what little he knew of the Masons, he could not object.
A Jew may not marry anyone who isn't Jewish. That being said. Free Masons are not a religious entity they are a club. I happen to know a married couple who are Jewish and are free masons. The free mason club or society as they call themselves don't require a specific religion only that you do have a religion and a belief in a higher power of some sort. For more guidance I would encourage you to look online for a chabad house nearby you which will be glad to assist you in learning about Jewishness, Torah, and life.