In Disney's Frozen movie, when Anna is running out of the palace, and through the gates, before Elsa's coronation, you can glimpse Rapunzel and Eugene in the bottom left hand corner. This leads to the conclusion that Arendelle and Corona exist in the same world and time period. 

However, there is more evidence that the two kingdoms are connected, other than a small cameo. 
In the Frozen II book, Forest of Shadows, the kingdom of Corona is mentioned several times. (If you do not know, Corona is the name of Rapunzel's kingdom.) 
Here are where it is used:
"In five days, Elsa would leave from the Arenfjord, the body of water on which Arendelle was built, sailing past Weselton and the Southern Isles before heading east to explore lands like Zaria, Royaume, Chatho, Tikaani, Eldora, Torres, and Corona."
Forest of Shadows, pg. 18, chapter 1, by Kamilla Benko

"Its great winds raised up high waves, and Anna and the rest of the crew covered their noses and mouths with the silk scarves that were originally meant to be gifts to the court of Corona, but now acted as shields so that they could breathe without inhaling sand as the royal ship glided closer."
Forest of Shadows, pg. 369, chapter 25, by Kamilla Benko

So yes, Corona most certainly exists in the Frozen universe.

In another Frozen II novel- Dangerous Secrets, the Story of Iduna and Agnarr- The King and Queen's excuse for going to Ahtohallan is that they are going South for the wedding of a faraway princess. Here's the part:
"Our story was simple: we were going on a two-week trip, to attend the wedding of a faraway princess by route of the Southern Sea." - Queen Iduna
Dangerous Secrets, pg. 362, chapter 48, by Mari Mancusi

While it was only a ruse, it still hints that they were going to a Princess's wedding; and since Rapunzel lives south of Arendelle, well...

There's also the matter of geography. Thanks to a satellite shot in the Disney tv show Rapunzel's Tangled Adventure, (a.k.a. Tangled the Series), we know that Corona is located in central France. Meanwhile, Arendelle is more obviously located in Norway, though this is unconfirmed, but the inspiration for the kingdom was drawn heavily from cities in Norway. 



Furthermore, though less useful, a legendary sword in Forest of Shadows is described as:
"And the blade...it was made of a blue-black metal- the same color as the meteorite in Sorenson's observation tower."
Forest of Shadows, chapter 22, by Kamilla Benko

The description of the sword (named Revolute) is very similar to a sword used by a warrior in the show Rapunzel's Tangled Adventure. In the show, a warrior named Adira has a sword called a shadow blade. 
Here is the description from the Tangled wiki:
"Shadow Blade is a magic, metallic sword made from black rocks; the one and only thing that slice through them with relative ease."
https://tangled.fandom.com/wiki/Shadow_Blade


As anyone who has watched Rapunzel's Tangled Adventure will know, the shadow blade is extremely strong, capable of slicing through rocks and trees. It has a metallic, blue-black blade. It is made from black rocks, which originate from the Moon Opal, which comes from the moon. 
The interstellar origins of the Revolute and of the Shadow Blade are similar, as they are similar in appearance. 


With all these facts, it is logical to assume that Corona and Arendelle existed in the same time period as well as in the same world. 
Rumors are now at rest: Arendelle and Corona exist together, and Corona is located in France, rather than Germany, as some theories claim.

The evidence is undisputed. 
Thanks for reading!