Really, what you're describing is kiruv, not proselytizing. The difference is that kiruv (often translated as "bringing close") is about reaching out to unaffiliated or non-traditionally observant Jews and encouraging them to take on Orthodox practices. In the not-so-Orthodox world, a lot of Jewish professionals use kiruv with a sort of tongue-in-cheek attitude that says something like, "We'd like to empower unaffiliated Jews to find meaning in Judaism of any kind in any way." That latter, semi-ironic way of looking at kiruv tends to be my approach when talking with people who aren't so Jewishly involved, and it sounds like it may be where you're coming from, too.
You're right that, technically speaking, your friend is Jewish. However, in one of the great confusions of modern Jewish life, ultra-Orthodox institutions would consider him as a Jew, but, for example, he wouldn't be allowed to go on a Birthright Israel trip because he was raised in another religion. Inviting him to your family's seder is a kind, generous and appropriate first step. It also might be the only step that ever makes sense for him and, in the context of your friendship, for you. Before the seder, talk to him a bit about what the night will look like and see if he has any questions. Emphasize that it's totally appropriate to ask questions during the seder and also that dinner is a good time to talk about some of the specific content of the seder ritual. During the seder, sit next to him, provide any relevant context about the holiday and make sure he knows where you are in the haggadah.
Afterwards, ask him what he thought in as open-ended a way as possible. Given that you've already put the idea in his head that this is his ritual, too, he may have a lot to say in a personal way, and he also might just try to take in what is likely a totally foreign experience without putting himself into it at all. Based on how he responds, you'll have a better sense of what else he might be looking for out of this newfound piece of his identity. Try not to put ideas in his head or words in his mouth about feeling ownership of any sort of Jewish identity. If he has a good time and seems excited, invite him to other holiday celebrations and Jewish activities, but try to keep those invitations in the context of, "I'm going to this thing, do you want to come?" rather than, "Come be Jewish with me." If he decides that Judaism is something he wants to explore, you'll be there for him and can help him find the right resources for study and community involvement. If he doesn't, you've still been a good friend and left the door open for him for the future.