No. “ Il ferait du soleil ” is basically the same as saying in English when asked about the weather  ‘it will make (some) sun’, and sounds as strange in French as in English.

It is ‘il faire (adjective)’ for the weather or ‘il y avoir (article noun)’ - so ‘ il ferait beau’ is correct here. 

Talking about the weather in French - il fait + [adjectif]

Talking about the weather in French - il y a + [nom]

 https://www.wordreference.com/enfr/sunny

Looks like you are wrong Maarten:

https://forum.wordreference.com/threads/it-is-sunny.351193/

https://context.reverso.net/translation/french-english/il+fait+du+soleil

I didn't say it is not in use - but it is not recognised as 'standard' French. 

One of those links seems to me to end up being mainly over whether 'il fait soleil' is correct, but many others point out that, to them, it is not. Most, not all, seem to me to be saying that 'il fait du soleil' is ‘wrong’ also. (Maybe that is my confirmation bias on a quick scan of the 2 links).

The other is an internet trawling, language scavenger site which supports the notion that 'poor, incorrect or non-standard' grammar is used often - surprise. There is also the problem of identifying whether the origin is metropolitan French or from another variation of French and the context of its entries

"ll fait du soleil ' is not 'usual' under the standard grammar "rules", and to many native speakers still sounds wrong. 

The lesson here also makes that clear, I think. So whether I am ‘wrong’ or not, you should aim your comment at the information provided here, not at me personally. 

Ultimately, this is part of the never-ending tug-of-war between descriptive and prescriptive grammar - if an expression is used often enough by a significant proportion of native speakers, it will become "correct" as a recognised expression in reputable references or by causing a 'tweak' to accepted grammar.

I think this has been discussed before with the result that il fait du soleil sounds like a 3-year-old would. Apparently it's a common mistake made by young children.

I have three Italki tutors this week. I'll ask them and report back.