Sorry for the delay, so if I understand: You had both
example.fr and setup
example.fr as the one you wanted to use with
example.eu being a parked domain as your trademark with a 301 to the site you were using. But, geo-changing situations and EU being a broader category you now want
example.eu as your site with content.
First thing you should know is how long will it take. My experience is maybe a month or so, with caveats and qualifiers. Google has been volatile as of late, with updates to the quality of their product search and other minor changes.
The last info I have from @GoogleSearchCentral #AskGooglebot
0:17 It seems that nothing's permanent in this world,
0:20 so how long is permanent when it comes to redirects?
0:24 At Google, we try to reprocess all pages 0:27 at least every few months.
0:29 Most pages are checked much more often.
0:32 However, the amount of crawling is limited
0:34 and there are many, many pages that we'd like to crawl,
0:37 so we have to prioritize.
0:40 When a URL changes, our systems need
0:42 to see the change in the form of a redirect for at least
0:45 a few times in order to record that change.
0:48 To be certain that a redirect has been seen a few times,
0:51 we recommend keeping the redirect in place 0:53 for at least one year.
Why so long?
Well around 20 years ago there were people up around this time who were cloaking pages, keyword stuffing, and at least one guy with a sites for Halloween store, Christmas store, and Valentines store that guy setup his Halloween site and valentines day sites to forward to his Christmas site, after Christmas he would forward to his valentines day site. The search engine they were waiting for was excite; They did a monthly update and at that time they turned a blind eye to cloaking and the update picked the winners and the losers. That changed when somebody started guaranteeing to put other people's sites at the top position in search engines. New York Times got interested and asked the search engines if other people could do that ... they said no because if users thought that was the case it would damage their brand. To satisfy the needs of marketers they gave us paid ads above the organic search results. In other words they cut out the middle man. And, tell the New York Times that they run advertisements first.
So search engines started processing redirects with a small degree of trust.
How to improve the process
All internal links should be pointed to the new URL, all external links you have control over, (all social media pages), should point their links to the new URL. In other words the change is not a temporary change till next month of indeed a long-term "permanent change."
When the change is seen as permanent that will change how search engines see the pair of sites. Sadly just putting the redirect on the
example.fr is not enough to be seen as permanent in the first few weeks.
And as noted in comments, WordPress has a setting for the URL that it uses to point to the main domain. That needs to be changed as to the new main domain ... it is a "Strong," signal as to what domain should be indexed.
After all changes have been made to signal the .eu as the page to be indexed so that the .fr is no longer to be indexed ... you can attract the robot by using https://search.google.com/search-console/not-verified?original_url=/search-console/settings/change-address&original_resource_id
Alternatively, one could keep both sites and put up unique content.
Another option is to remove the 301, keep both sites, and refer the users of
example.fr that there is new content at
example.eu. and on occasion put new content on
IE that guy with the three store, could put up a notice that Halloween products are sold out and they have new deals at Chrismas-at-[our-band].com