Le jeu de société suit le jeu de cartes.

Because both noun phrases are being used as specific singular nouns.

• jeu is a masculine singular noun, so its definite article is le.
• le jeu de société = the board game
• le jeu de cartes = the card game

French often repeats the article where English might also use the twice. There is nothing unusual here: one le belongs to the subject, and the other le belongs to the object.

Yes, literally it looks like game of society, but jeu de société is the normal French expression for board game or, more broadly, a tabletop/social game.

So this is a vocabulary item you mostly learn as a set phrase:

• un jeu de société = a board game
• les jeux de société = board games

The literal pieces do not match English word-for-word, so it is best to treat jeu de société as a standard expression.

French often builds this kind of expression with de:

• jeu de cartes = card game
  literally: game of cards

This is very common in French. English often uses one noun directly in front of another noun (card game, chicken soup, stone wall), but French usually connects them with de or another structure.

So here:

• jeu = game
• de cartes = involving cards / of cards

Because in these fixed expressions, the noun after de is being used to describe the type of game, not a specific thing.

Compare:

• un jeu de cartes = a card game
• un jeu de société = a board game

Here, de introduces a category or characteristic. French often leaves out the article in this pattern.

If you added an article, it would usually change the meaning:

• un jeu de cartes = a card game
• un jeu des cartes would sound wrong here

So in these expressions, the no-article pattern is the normal one.

That is just how these established expressions work.

• jeu de cartes uses cartes in the plural because a card game involves cards in general.
• jeu de société uses société in the singular because it is part of the fixed expression for board game.

This is not something you can always predict from English. It is better to memorize the whole phrases:

• un jeu de société
• un jeu de cartes

suit is the third-person singular present form of the verb suivre, which usually means to follow.

Conjugation in the present tense:

• je suis
• tu suis
• il/elle/on suit
• nous suivons
• vous suivez
• ils/elles suivent

So in your sentence:

• Le jeu de société suit le jeu de cartes.
• The board game follows the card game.

The subject is le jeu de société, which is singular, so the verb must be suit.

No. French suit is pronounced differently.

A rough guide is:

• suit ≈ swee

More exactly, the French sound is /sɥi/, which has a glide that English does not use in quite the same way.

A simple pronunciation breakdown of the sentence is:

• Le → luh
• jeu → zhuh
• de société → duh soh-syay-tay
• suit → swee
• le jeu de cartes → luh zhuh duh kart

That is only an approximation, but it helps.

Yes. This sentence follows the basic subject + verb + object order:

• Le jeu de société = subject
• suit = verb
• le jeu de cartes = object

So structurally it is very close to English:

• The board game follows the card game.

That makes this sentence fairly straightforward grammatically.

Because the subject is singular:

• Le jeu de société = the board game = one thing

So the verb must match a singular subject:

• Le jeu de société suit...

If the subject were plural, you would use suivent:

• Les jeux de société suivent le jeu de cartes.

So the verb form depends on the number of the subject, not on the object.

It can mean both, depending on context.

suivre can be used for:

• physical following
  
  • Le chien suit son maître. = The dog follows its owner.
• order or sequence
  
  • Le chapitre 2 suit le chapitre 1. = Chapter 2 follows Chapter 1.

In your sentence, the exact nuance depends on context. It could mean:

• the board game comes after the card game
• the board game follows the card game in order
• possibly even that it is played after it

So suivre is broader than just literal physical movement.

Yes, if you are speaking more generally or using a different determiner.

Examples:

• Un jeu de société est sur la table. = A board game is on the table.
• J’aime les jeux de société. = I like board games.
• Ce jeu de cartes est ancien. = This card game is old.

In your original sentence, le is used because both noun phrases are presented as definite: the board game and the card game.