I lied. It wasn't the French sonnet I was thinking of, it was the Italian sonnet. Like the English sonnet, it has fourteen lines... The rhyming scheme is A B B A A B B A C D E C D E. I don't even know if there is a French sonnet. There's probably one out there somewhere.
The Italian Sonnet is also known as the Petrarchian Sonnet. The English one is much more flexible, since the Italians liked to structure theirs such that it had two parts, 8 lines than 6 lines. The English could do 4 4 4 2, 8 6, or other weird combinations.
Basically to sort out which is which, English sonnets tend to have the final two lines as a rhyming couplet.
Apart from structure, poetry can be sorted out into many variations, such as Renaissance Poetry, which tends to make use of conceits (long extended metaphors between objects that are otherwise unrelated), tend to have love as a central theme, might use religious or nature based imagery, and might mention the Divine Right of Kings.
Example of Renaissance Poetry:
When Love with unconfined wings
Hovers within my Gates ;
And my divine Althea brings
To whisper at the Grates ;
When I lye tangled in her haire
And fettered to her eye ;
The Gods that wanton in the Aire,
Know no such Liberty.
When flowing Cups run swiftly round
With no allaying Thames,
Our carelesse heads with Roses bound,
Our hearts with Loyall Flames ;
When thirsty griefe in Wine we steepe,
When Healths and draughts go free,
Fishes that tipple in the Deepe,
Know no such Libertie.
When (like committed linnets) I
With shriller throat shall sing
The sweetnes, Mercy, Majesty,
And glories of my KING ;
When I shall voyce aloud, how Good
He is, how Great should be ;
Enlarged Winds that curle the Flood,
Know no such Liberty.
Stone Walls do not a Prison make,
Nor Iron bars a Cage ;
Mindes innocent and quiet take
That for an Hermitage ;
If I have freedome in my Love,
And in my soule am free ;
Angels alone that sore above,
Injoy such Liberty.
Richard Lovelace's
To Althea From PrisonOr one other poetry form is the epic, such as Homer's Odyssey, or Milton's Paradise Lost. There are hundreds of other ways to characterise poems.
My advice for reading is not to care about structure, but just let it flow over you naturally.