Prestashop has always been a bit slow, but there are some things you can do.
1. Go to admin > advanced parameters > performance > force compilation turn it off (first option) and at “cache”, select “yes”. Save.
You should notice that your store loads much faster now.
Other things. From admin > modules > theme configurator > disable quick view.
Also from admin > advanced parameters > performance > optional characteristics, turn all 3 of them to off.
From CCC (below), enable everything.
Now go to https://gtmetrix.com and run a check on your website.
You will be able to minify the css, replace the css files with the one you get from gtmetrix.com.
You can also minify the javascript, also replace the minify version provided by gtmetrix.com.
Replace dynamic sql queries
2. You can try to replace the code from footer.tpl with normal html code after you copy/paste the html source code from your website.
What you need to replace is “{$HOOK_FOOTER}” with the html code (it includes the newsletter part), you can just delete “{$HOOK_FOOTER}” and see how your website looks. You will have to delete the cache from admin if nothing happens. Be sure to have a backup before doing these changes.
You can do the same with header.tpl.
3. Go to admin, modules, select “installed modules” and start to disable modules that you don’t use at all. Keep a track.
4. If you want to disable/delete from the javascript scripts from header, just rename them and they will stop to appear in the code. For example js/autoload, rename it as autoload2. Same with css links from the header. Notice that autoload will affect view grid/list in categories. If you don’t use this feature, you can disable autoload.
5. Start to minify all the css you find from source, header. You can use https://cssminifier.com/. Be sure to have backup to your files.
6. Start to minify all the javascript files. You can use http://jscompress.com/.
If nothing works, just move the website to a new webhost, located in your country. If your store is for customers from Germany, move it a webhost that is located in Germany.