In Episode 2, as Jean shows Nadia his airplane at his workshop, he talks about how it is his eighth attempt — he sacrificed his seventh at the competition. Cheerfully, Jean says it was worth it just to rescue her. Nadia replies "thank you for that!"
Later, Jean tells her he is going to take her to Africa aboard his plane. Nadia is uncertain, asking "Really?" But when she sees Jean's genuine smile and determined look, she blushes, appreciating his kindness.
In Episode 5, after they are shot down over an island, Jean is slumped on a tree. Nadia tearfully kneels over him, looking worried.
Before surrendering to Gargoyle's soldiers in episode 6, Nadia entrusts Jean with the Blue Water, telling him that she will wait for him to rescue her, and gives him a kiss on the forehead. "Mama's kiss," she says.
Sanson and Hanson set out in the Gratan to save the Nautilus from being destroyed in Gargoyle's mine trap, but not before subduing Grandis. Their reason? They want to protect her from getting killed. Shows how far these three are inseparable.
Two little moments in episode 11: after Jean talks briefly with Nemo on the deck of the Nautilus, Nadia smiles softly at Jean. Later on, at the end of the episode, as Jean reflects on Electra's words, Nadia asks him "What's wrong? You're so quiet." She also questions "Is this a good ship or a bad ship." Jean replies "I believe that it is a good ship...because the captain is a good man."
In episode 12, an Accidental Pervert gag ends up with Nadia throwing a stone to Jean on the mistaken belief he was sneaking a peek on her. The stone actually hits Jean in the face, and Nadia turns mortified at seeing she has hit him for real. Even if it is treated as just a throwaway gag, it shows that although she sometimes berates him beyond the reasonable, she really cares for him, even more than she thinks herself.
Even better, she and Jean go on a walk to get over this embarrassment and are seen enjoying each other's company.
The 16th episode: "The Mystery of the Lost Continent" has possibly the most heartwarming scene in the entire series:
The revealation that his father died years ago, at sea, saddens Jean, leaving him feeling that all his efforts were for nothing. So he tells Nadia he no longer sees any point in inventing and has decided to give it up; which saddens her because she knows how much it means to him. So she cleverly reminds him of the promise he made to her to cheer him up, in her best Jean impression. It works.
The scene itself, and the accompaniment of 'To Home', makes it so poignant, that you might find yourself getting a little misty.
The 17th episode: "Jean's New Invention" shows Nadia continuing to bond with Jean as she encourages the latter to build a gyrocopter, inspiring him to invent again. She even brings him some (half-baked) seaweed to eat (to apologize for scolding him for missing dinner). The end of the episode shows both on a glorious gyrocopter flight with Jean promising to take Nadia to Africa. She is, needless to say, delighted.
In episode 31, "Farewell, Red Noah", Nadia hears that Jean has come back to save her from Red Noah, and begins weeping for his safety. The mysterious voice asks Nadia "is there something more important to you than the Blue Water." Nadia nods yes, and then in the next scene, she tearfully runs into Jean's arms, not even caring that he's seeing her nude.
In episode 35, where Jean tells Nadia he loves and accepts her for who she is, even after she admits her connection with Neo-Atlantis. Then they discover they've arrived on Nadia's birthday and sing "happy birthday" to her for the first time in her life. (In the dub, it's redone as "It's your birthday today.")
Actually, this can apply for any scene where Nadia acts kindly toward Jean.