I've got a Debian web-server with Apache2 installed and want to occur one directory DirectoryIndex to .html file (exactly this title - .html). However when I attempt to spread out page from browser it send 403 error. I have transformed apache2.conf (set to permit .ht files), I placed .htacess file in directory and occur it:

DirectoryIndex .html index.php index.html
AllowOverride All
Order Deny,Allow
Allow from all

However it still not work and shows 403 error. Things i doing wrong and things i forget to complete?

It is:

<FilesMatch "^\.html">
        Order deny,allow
</FilesMatch>

DirectoryIndex .html

Seems like you've got a rule somewhere inside your apache file that denys use of files beginning having a .. This generally is a Positive Thing, as many sensitive files begin with dots (ie: .htaccess, .svn, .git, .htpasswd, and so forth).

You may have the ability to circumvent the problem with something similar to this:

<FilesMatch "^\.html">
 Order allow,deny
 Allow from all
</Files>

Disclaimer: This appears just like a hack. I'm not sure what you are attempting to do, there is however most likely a cleaner, less error prone method of doing it.