French agreement has nothing to do with opinions; it’s a grammatical function of the language. Just as verbs change to agree with their subjects in most languages (“I am” vs “you are”), so too do adjectives and pronouns in French: they change to agree in gender and number with whatever word they modify or replace (un homme fort vs une femme forte).
One of the eight parts of speech, adjectives are a type of modifier; that is, they modify or describe nouns in a certain way, letting you know the size, shape, weight, color, nationality, or any of a myriad other possible qualities of nouns.
By definition, adjectives modify nouns. But more than 30 French adjectives can sometimes modify verbs instead, thus taking on the role and characteristics of adverbs, including the fact that they are invariable.
Most French verbs are conjugated with avoir as their auxiliary verb in compound tenses and moods, and therefore do not require agreement with their subjects. But avoir verbs do need agreement in a very specific construction: the past participle must agree with the direct object when it precedes the verb.
The three French verb constructions which include some form of être plus a past participle usually require grammatical agreement of the past participle with the subject.
Verbs of perception are subject to grammatical agreement in the compound tenses, but the rules are somewhat tricky - they only agree with their subjects when they precede the verb.
An article is a word that modifies a noun in a particular way, by stating whether the noun is specific, unspecific, or partial. There are three types of French articles, and they all agree in gender and number with the nouns they modify.
The French definite articles (le, la, l', les) indicate either a particular noun or, contrarily, the general sense of a noun. They're used similarly to their English counterpart "the," but there are many instances where a definite article is required in French but not English.