Depends on the company that put the DVD out. Refer to this handy guide compiled by Habers:

Twentieth Century Fox - Reversible Cover, English one side, French
on the other side

Alliance Atlantis (Distributes Miramax, New Line Cinema, Artisan
and Dimension Films in Canada) - Single Side Bilingual Covers and
sometimes reversible covers. However these reversible covers are pointless
since both side are still bilingual with French or English being more
visible.

Anchor Bay - Distributed by HGV in Canada. Release the same covers
as in the US

Buena Vista - Separate French and US Packages

Lionsgate Films - Separate French and US Packages. The content of
the DVD, in both cases, stay the same

Columbia Tristar Home Entertainment - Separate French and US
Packages

MGM - Separate French and US Packages. The content of the DVD, in
both cases, stay the same

Paramount Pictures - Single Sided Bilingual Covers

TVA Films - Separate Covers and Reversible Covers. Sometimes even
including the choice to the viewer to check out his menu in English or
French

Artisan (Distributed by Alliance Atlantis) - Single Side
Bilingual Covers and sometimes reversible covers. However these reversible
covers are pointless since both side are still bilingual with French or
English being more visible.

Koch Vision - Single Sided Bilingual Covers

Warner Bros. - Separate French and US Packages. The content of the
DVD, in both cases, stay the same

Universal - Reversible Cover. Both sides contain English AND
French with one taking more precedence over the other

Miramax (Distributed by Alliance Atlantis) - Single Side
Bilingual Covers and sometimes reversible covers. However these reversible
covers are pointless since both side are still bilingual with French or
English being more visible.

New Line (Distributed by Alliance Atlantis) - Single Side
Bilingual Covers and sometimes reversible covers. However these reversible
covers are pointless since both side are still bilingual with French or
English being more visible.

Dreamworks (Distributed by Universal) - Reversible Cover.
Both sides contain English AND French with one taking more precedence over
the other

Info taken from www.canadiandvdgroup.com