Who may enter a love relationship with Josephine? You can enter a relationship with Josephine regardless of your sex (she is bisexual). You can also play as a character of any race.
How to build positive relations with Josephine? You do not need to watch your steps in any particular way, while meeting with her. Simply, try to exhaust your dialogue options and agree with her opinions.
More important steps:
- Josephine cannot be a party member so talk to her at the Inquisition's HQ (first Haven and then Skyhold) each time after you return after a longer journey. After you have sufficiently developed your relations with her, you get the opportunity to complete her first quest - Of Somewhat Fallen Fortune. Complete it and see Josephine again. The meeting should end in a kiss.
- Talk to Josephine and especially look out for opportunities to ask her about her Orlesian heritage. This way, you will gain access to her second quest - Heraldry from a Herald. You need to complete this quest as well.
- You need to wait until you get the last quest from Josephine. It is An Unexpected Engagement and you learn from Josephine that her parents intend her to take an arranged wedding with Lord Otranto. You need to complete this quest by challenging the nobleman to an honorable duel. Josephine appears after you start the duel and you need to take the most important decision, at this point - whether you want to express your feelings and commit yourself, or let it go.
- While completing the Wicked Eyes and Wicked Hearts quest, you can play a short prelude to the affair with Josephine, i.e. dance with her in the Winter Palace.