Can someone answer this for me? Really important about the burning scene

I thought they did make her say those things in this miniseries.

Or...I just shoot you - "baby."
- Scully

She did call out to God, not specifically Jesus, and then she suddenly became calm and peaceful.

God giveth, and the DMV taketh away!

There's a 1970 Russian adaptation of Joan of Arc called "Nachalo" that depicts a fairly accurate Joan-at-the-stake scene. It shows her with her head shaved and a heretics cap, which was usually placed on the heads of people convicted of heresy, though I don't know for sure if Joan had one placed on her, but it's likely.
There's a clip of her burning, in Nachalo, at Youtube http://www.youtube.com/watch?v=hG1aRfG9hvw

The most accurate one, overall, was The Passion of Joan of Arc, which showed the actual words she spoke at the trail and at the stake.
An actual depiction would show her, most likely, gasping for air as she suffocated from the smoke as well as her cloth-gown burning away from her body, but showing that would be viewed as disrespectful and possibly vulgar. In the TV version they do show her gown starting to burn away from her, which is the only version, I've scene, that takes note of this.

In the TV version she asked for a crucifix, when, in fact, they gave her a cross. A crucifix is a cross *with* a crucified Jesus on it. She also did call out to Jesus several times, in real life, but she only said his name once in this version, I suppose they did this to be politically correct.
Also, it was a clergy man named Martin Ladvenu who held-up the crucifix for Joan, not Jean de Metz, who wasn't even at her trial or execution

Try the page below which has the execution scene from Joan of Arc with Ingrid Bergman
http://www.maidofheaven.com/joanofarc_videos_burning.asp

In this version, she does ask for a crucifix to be raised to the level of her eyes, and then cries out "God" and "Jesus" several times as the flames engulf her. It's heartbreaking because we're so used to seeing paintings and portrayals of Joan looking and acting all serene while she burns. In real life she most likely screamed and cried as depicted here.

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Because unless you were actually there at the time and videoed her death, you are relying solely on biassed historical accounts of the event, many written by people who were either not there themselves, or not even born at the time...
No-one can say for sure exactly what she did.