Well here is the rest of my summary, so hopefully it will answer your question!
I watched the rest of the movie again yesterday before going to bed, and just like the last time, I had some crazy dreams!
But it was worth it since I had gotten somewhat lost the first time because I had watched it bit by bit, I didn't know on which planet I was at some point! :huh:
Oh by the way fafner, I've seen the tranformation ring in the middle of the story, so you were right, it seems necessary for inhabitants of Améthyste to turn themselves into something else.
So, here is the second part of the story and, obviously, a big spoiler!
It's when I write long texts like this one that I feel that my English is really lacking!
Hopefully it will shed some light on a very cryptic movie.
On Pomona, Musculo asks "Baba au rhum" ("Rum Baba", usually "Hamegg " in Tezuka's world) to put Vif-Argent in jail. Musculo is an Earth reprensentative who had kidnapped Florianne because he wants to conquer Pomona. If the king of Pomona won't obey him, Musculo will make the Earth attack Pomona. By freeing Florianne, Vif-Argent has gone against his plan.
In jail, Vif-Argent meets Professor Aquarium, a genius who has a lot of interesting information to share. You may want to read fafner's translation of this conversation in his November 28th post because I can't do a better job. 
Meanwhile, Florianne's father tries to convince her that her love for Vif-Argent is unrealistic. It's worth mentioning that he doesn't like earthlings (for good reasons! ). He explains her that they are different from earthlings, that if they get injured, they can recover by planting their roots in the soil and not move from there. But Florianne doesn't care. A little later, Musculo lies to Florianne, telling her that Vif-Argent has left Pomona. Florianne suspects he is responsible for this and also accuses him of hurting her father. He propose to her, telling her it would make the relations with Earth better, but she refuses. At that point, Jack, who has just landed on Pomona, orders Musculo to let go of her.
After Vif-Argent and Professor Aquarium escape from jail, Professor Aquarium tells him about his "evil powers". They are several bottles in his laboratory. One of the bottles contains "terror", which includes fear of loneliness, of illness and of lack of money. If the terror gas was spread, it would cause those who would inhalate it to be terrified. Vif-Argent then finds Florianne The pink creature doesn't want to help him reach her at first, but she relents.
Musculo and "Baba au rhum" heard what Aquarium told Vif-Argent and decide to steal the terror bottle. Then, from a spaceship, Musculo threatens the king of Pomona: he'll make the bottle explode on Pomona if the king doesn't resign (in order to take his place, of course) and let him marry Florianne. At that point, Jack attacks them from his own spaceship and asks them to give him the terror bottle. Instead, they run away into outer space. Vif-Argent and Florianne are brought to Jack's spaceship, where he orders Vif-Argent to help him catch Musculo. Instead, Vif-Argent intends to stop Jack from attacking planets, but he can't bring himself to shoot Jack, who was expecting he wouldn't. Both spaceships meet comets brought by a distant black hole. Musculo's spaceship breaks up as it was approaching Earth and the planet is soon covered by the terror gas.
Jack and Vif-Argent land on Earth, however they find themselves mistakenly in the past. Vif-Argent escapes with Florianne (and the pink creature), but Jack forbid his men to shoot them because "they are only children". Soon after, Vif-Argent and Florianne get attacked by monkeys, but Jack rescue them. Using a time-travel machine, Jack then brings them in the future. (The weird images on a blue background you see at that point are nightmarishes images caused by the terror gas.) Jack asks Vif-Argent what was his father's name, and Vif-Argent replies "Kudor", adding that he'd like to meet him. Jack agrees and brings him to Kudor's house in 1980, the year of Vif-Argent's birth, but warns him to not do anything that could cause the future and their own fate to be changed.
There is a lot of pollution on Earth. The planet is controlled by a machine called grandmother ("grand-mère" in French). Earth's president Vidor does everything according to what the machine says. He asks it who's the greatest man on Earth and the machine answers "Kudor". Kudor is against the machine and those who support it and conquered space, and thus the machine also says Kudor should die. In a meeting with President Vidor, Kudor explains that people are poor and that the planet is threatened by wars, pollution, racism and drugs, among other things. Vidor tells him that if he opposes the logic and program of the machine, it could be dangerous for him. Kudor then accuses Vidor of having kidnapped his first-born son but says that he'll continue to oppose him anyway. Kudor goes home to meet with his wife and second born baby. He plans to ask other planets to help him fight to free Earth from grandmother because even if earthlings all fight together, they won't be able to succeed by themselves.
Before entering Kudor's house, Vif-Argent wants to prevent Kudor from being killed, but Jack warns him again that doing so would bring chaos. Vif Argent agrees. In the house, Vif-Argent sees himself as a baby in a cradle. His parents gets in the bedroom while he's still there. Despite his promise to Jack, he tries to convince them to stay on Earth because they'll get killed, but they don't understand who he is, why he calls them "mom" and "dad" and what he wants, so they leave to board the spaceship anyway
but not before his father told him about their first-born son who has been kidnapped by his ennemies. His father said he keeps thinking of him, but had to sacrifice him to keep on fighting. He would be 5 years old by then, and his ennemies have scarred his face.
Vif-Argent returns to the time-travel machine, crying but having understood that Jack is his older brother. Jack doesn't like to be called "brother". He says he had understood they were brothers when they first met (but then I wonder why did Jack look so surprised when Vif Argent told him his father's name
? :huh: ). He had been kept hostage by Vidor until he escaped at age 20.
Vif-Argent would still like to save their parents, but Jack refuses. However, Jack adds that they could change the future. Therefore they go in the "present", in 1997, to fight grandmother. But this won't be easy, because grandmother can detect any living being within one kilometer of it and electrocute him instantly. However, grandmother can't detect anyone at less than 50 meters from it. They will use the time-travel machine to reach that point. Jack says he started attacking planets because he needed money to buy the time-travel machine to free Earth. (Interestingly, he had said earlier that he had stolen the machine from a space travelling merchant, so apparently he spent all those years stealing money for nothing! 
). They'll have only one minute to destroy grandmother.
During the battle against Vidor and his men, in order to reach grandmother, Florianne gets badly wounded. Then, Jack loses his gun and Vif-Argent is the only one left who can destroy grandmother. At one point, grandmother appears to him as his sister Étoilia to fool him and starts hypnotizing him, but Jack wakes him up. Vif-Argent finally manages to destroy grandmother, while Jack, badly wounded, tells him to run away because the machine will blow up and that his fate is to die this way. And era of peace and happiness begins on Earth.
Florianne is wounded, but as an inhabitant of Pomona, she's made of chlorophyll in other words, she is a plant looking like a human, so she asks Vif-Argent to plant her on the bank of a nearby lake. There she feels better, saying she'll get leaves and soon become a beautiful tree. She asks Vif-Argent to sow her seeds in the fall, everywhere, so her children will cover the Earth in a forest. She then asks Vif-Argent to forget her and be nice with Étoilia. Vif-Argent is stunned that she knows Étoilia, but Florianne wont tell him how she got to know who Étoilia was, only adding that his sister is alive, close to him and loves him. Florianne becomes a tree and Vif-Argent finally recognizes Étoilia in the little pink creature that saved him so often.
In the end, the narrator, I think its Jacks voice, says that its too late to change the past, but that its not too late to change the future, starting from today.
The End.
My comments (still a spoiler):
It's interesting that this movie was made in 1978, just two years prior to the color remake of Astroboy. It's very reminiscent of the brotherly relation between Astro and Atlas, where the "bad" brother turns up to be not that bad after all. It reminded me a lot of "The Girl from Alsoar" as well. I had always thought that this human-turning-into-a-plant thing came out of nowhere, but in this movie, it turns out to be much more poetic!
).