I have much money.

I have a lot of money is the more correct phrase of the two.

I've much money is an awkward and unlikely to be used expression and might tip off some one that you're not a native speaker.

Also, it's probably not wise to say that in a group setting. Someone might try to lighten your load, that's not a good thing.

I have much money

I'm very happy for you. I hope you get a chance to enjoy it.

"Much money" used positively e.g. "His family has much money" is not incorrect; it is simply very unidiomatic and formal and as a result very old-fashioned, so much so that most people would not think of using it, especially in conversation. It mainly survives when used with a negative: e.g. "I don't have much money", or in phrases such as "however much money you have", "There is much money saved in banks".

What's with the eye-rolling? People up to about 1900 or so, especially those of the upper class would have probably said things like "His family made much money from shipping."

if you check again, the eye roll was deleted.

Yes, you're right, it's gone.

It's not about the matter of logic, but the one of common-ness, I guess, right?

Now that I've realized it could tip off people that I'm not a native speaker,
I should try not to say that. Thanks Ragman.

Of what you said, could I ask you what the meaning of 'lighten your load' is?

My dictionary says 'lighten one's load' is 'make a difficult or upsetting situation easier to deal with', and I have no clue why you finished your sentence, adding 'that's not a good thing'.

Could you please help me understand what I misunderstood?
Thank you, glitterbag.

I just wish I could be just like that. Thanks Setanta.

Sometimes attempts at humor from American (or an English-speaking) culture is not understood by a non-native speaker. The phrase (in this person's explanation) 'To lighten your load' means to take some of that excess money. So if you the speaker makes a statement about having much money, someone dishonest might want to steal or help balance their budget.