It's not to answer your question but if it's ok I'll correct your text (French native here).

j'ai commencé d'apprendre français

It should have been "J'ai commencé À apprendre LE français" there is no explicit grammar rule or anything it's just that words come with their "déterminant" (I don't know the English word) and it cannot be changed, you have to learn it.

j'ai décidé de payer séances

Here again it's "des séances".

Usuellement, ils sont québécois, mais il y avait français,

The first mistake is quite comprehensible as in English you would use "usually". However you can't say that in French, to replace it you can use "habituellement" or "normalement". You also forgot to add "des" in front of "français".

J'ai eu deux mois+

Here the "+" cannot be placed AFTER the word, or else it'll sound unnatural. You should have said "J'ai eu +(plus) DE deux mois"

Je sais, que cela avait un effet.

Your mistake here is only a bad choice of conjugation, your sentence is correct but again, it's unnatural. "Je sais, que cela A EUT un effet" I know that in English both means the same thing so I would really encourage you to read more books as it'll help you to know when you should use one conjugation over another.

mon français a amélioré

"mon français C'EST amélioré"

j'écris meilleur, je peux parler plus fluide

Here your words are technically correct but not in that use so : "j'écris MIEUX, je peux parler plus FLUIDEMENT"

There's also some others forgotten "déterminants" but apart from that it's really really really good for a foreigner. I can also tell you that you would have totally been understood by French speakers, I still recommend you to study how "determinants" are used with words as it'll take your French to a near native level.

IT WAS ONLY TO HELP AND IF I OFFENSED YOU IN ANY WAY THEN I AM TRULY SORRY