Do people speaking languages with simple grammars have lower intelligence than people speaking languages with complicated grammars?

No - why would you think that?

The grammar of a language tends to get simpler as the language gets older. This is not universally true, but it is true by and large. For instance, Middle English was more complex than Modern English. I suspect the same is true for most of the Romance languages also. "Simpicity" has nothing to do with people's intelligence, but has more to do with the age of the language.

No child considers his or her native language to be difficult. Yes, some are easier, notably Bahasa and some Polynesian languages, but many are incredibly complex like those of some of the Native American and Siberian peoples.

I'm simple-minded.
Technically a complex word or sentence contains a Main part and one or more other parts.
As for the verb, it is a word or phrase indicating what somebody does, what state somebody is in, what is becoming of somebody.

That is somewhat true because children who learn two or more langauges when young develop the language part of the brain more than others, so a child who learns a foriegn language before the age of five is better equipped mentally to learn more languages in later life.
Therefore a person who speaks a complex language probably has a more developed brain in the area of language.
However, since different parts of the brain develop for different skills, a person who speaks a simple language may still be a better mathematician or engineer.

GAWD, Intelligence is the ability to Stay Alive, To continue to Exist against hard times.

The people who pass tests, that do not involve life lessons are just "Show Boaters".
Communication is an ability for life, not some sort of be all.

It has nothing to do with intelligence.

Ummmmm no. Not at all. Intelligence is not defined by the language you speak. Learning another language on top of your native language can make you smarter but...not much I guess. All children who learn their native tongue think it is easy. English could be considered an easy language with respect to grammar but some of the most brilliant minds were native english speakers. Smaller more isolated populations tend to have languages with more conservative grammatical structures... which many would equate to being difficult. Honestly, someone who speaks, let's say Finnish (highly inflected) isn't naturally smarter than a, let's say English speaker. They both can produce complex thoughts and ideas in their mother tongues proficiently. Their language is different, makes them think differently...not more efficiently. Ie: english uses prepositions, Finnish uses post positions. Postpositions are considered hard because they're a different structure than we're used to...not naturally hard

By your definitions English might come into "simple grammar". It has only 2 tense forms, though many tenses formed by auxiliary verbs. It has in general no gender for non-animate nouns, unlike other European languages which allocate grammatical gender to all nouns.