What is the plural of "Mars"?

As MT_Head points out in the comments, you may be able to avoid using a plural form by resorting to phrases such as ""Mars helicopter configurations" or "Mars configurations." But to answer the question that you actually posed:

Marses?

Even though it sounds a bit funny, Marses is certainly one valid plural form. This follows the default English rules for forming a plural, which have us add /ɪz/ ("izz"), spelled "es" (or just "s" if there is already a silent e) after the sounds /s/, /z/, /tʃ/ ("ch"), /dʒ/ ("j"), /ʃ/ ("sh") or /ʒ/ ("zh"). By convention, we fall back to these default rules when pluralizing proper nouns with no commonly used plural forms. (Source: the "Daily Writing Tips" online post "Plurals of Proper Names" by Mark Nichol. There is also another question on this site that seems particularly relevant: Pluralization of names)

Here are the examples I've found so far online of Marses being used as the plural of Mars. (All books cited were accessed through Google Books.)

For the family name "Mars":

• "Veronica Mars: When both Marses failed", a post by Alan Sepinwall from his blog What's Alan Watching?.
• "You turn up anything more on the Marses?" from The Black Ace: A Brad Shade Thriller, by Gare Joyce.

For the god Mars:

• "Like so many little Marses, / With their tilters at their a–s," from "Helter Skelter," a poem by Jonathan Swift, collected in "The works of the English poets, from Chaucer to Cowper," edited and with prefaces by Samuel Johnson.
• "The ancient patriarchs, afore the flood, [...] become stout Marses, and beget young Cupids." From "The Alchemist", by Ben Jonson, collected in The Works of Ben Johnson, with notes and a biographical memoir by William Gifford.

For the planet Mars:

• "It explores relationships among the Marses seen with the naked eye, through the telescopic lens, and with the mind's eye as well as the various Marses that have been perceived–or created–by scientists, writers, and visual artists[...]" from Imagining Mars: A Literary History, by Robert Crossley.
• "They had themselves already dreamed Marses more radical than any she could believe in, Marses that were truly independent, egalitarian, just and joyous." From Green Mars, by Kim Stanley Robinson.

Mars?

Thanks to Edwin Ashworth, it's been brought to my attention that in some contexts, the invariant plural Mars, with no apostrophe, has also been used.

In particular, this has been used when referring to the "Martin Mars" flying boats/water bombers/tankers/seaplanes. I'll try to find more citations and examples of this, but this might actually turn out to be the most relevant situation for you, as it's an example from the context of aircraft.

At first I wondered if there might be some convention to never use a distinct plural form of an aircraft name, but from what I can tell there isn't: a pluralized form of the aircraft Martin P5M Marlin, "Marlins", is used on the site of the National Naval Aviation Museum (located in Florida in the United States of America).

So it's possible that people simply thought "Marses" sounded wrong in this case.

Why it doesn't have an apostrophe

It could not be Mars' because a single apostrophe is never added to a word to form a plural; this is only ever used for forming possessives.

An apostrophe plus s ('s) is also generally only used to form possessives, although besides this it is sometimes used to form plurals in highly restricted circumstances: after a numeral, a single letter of the alphabet, or an abbreviation ending in a capital letter or a period. (I didn't quite cover everything; here's Wikipedia on apostrophized plurals.) In any case, Mars is none of these, so Mars's is also not correct as a plural form.

Other options?

If you go with the (highly inadvisable) Latin plural, Wiktionary says it would be Martes (which would be pronounced in an English language context as /ˈmɑrtiːz/ (the same as "Marty's"). I'm just listing this for fun.

I'm not sure where I got the idea of Mars' from.

Early in the last century, perhaps.

It did once used to be acceptable (and earlier still, quite the done thing) to use an apostrophe when pluralising proper names, especially if they end in s, and so Mars's. You may have seen enough Jones's etc. to half-remember it and come up with Mars' instead of Mars's.

The form is beyond old-fashioned though, to the point where it is probably not really acceptable today. Go with Marses.

Or dodge the issue and go with "Mars configurations".