Translations for instantaneous in French

Here are paragraphs from public domain books translated:

Then when the letter was sent I went out as if to free myself from the instantaneous remorse of this infamous action.	Puis, quand cette lettre fut portée, je sortis comme pour me soustraire au remords instantané de cette infamie.
The Lady with the Camellias, by Alexandre Dumas son	La Dame aux Camélias, de Alexandre Dumas fils