Are you familiar with the Merriam-Webster Online Dictionary? It has a nice audio feature; it will let you hear the preferred pronunciation for words. If you go here:
you'll be able to hear that there are two versions that are considered valid in English (with the accents on the either of the last two syllables).
However, I'm honestly not sure how to get you the pronunciation in French. I suspect it would be "sa-lome," like "shalom," but since French allows you to add accents on specific syllables, you could accent it various ways depending on the namer's intent.
You can pronounce Salome by sounding it out in the following way:
Sa low may
The big question is whether or not there is an accent on the last "e". If there IS an accent, it is sah-loh-may (note that all the syllables have equal stress in French). If there IS NOT an accent, it is sah-lohm (again, equal stress on each syllable). HTH!