verbs are accepted from a power at different period and according on the influence of an agreed area.
strongest people give the right form, weakest are forgotten.
finissais = finissoi = finiffoi = finissasse
ss = ff in old french so it is a recall of the noble origin of the language i suppose … toutes les conjugaisons découlent des unes des autres, cela permet le passé simple et le plus que parfait d’où le souci d’homogénéité par l”emploi des ss et des mêmes terminaisons.
fr has a genuine & original evolution coming from gr:lat.

French conjugations come from Latin, with more or less differences (it’s more direct in spanish by example) depending on tenses and verb group.

Have a look at “amare” here, and compare with French “aimer” there.

1. Amo ====> j’aime
2. Amas ===> tu aimes
3. Amat ===> il aime (lost the ending t a long time ago)
4. Amamus => nous aimons (something like amus => aums => oms => ons)
5. Amatis => vous aimez (something like atis => aits => aiz => ez)
6. Amant => ils aiment

NB: Latin short “a” often became “e” in French…

Formation with to be and to have

In latin, lots of tenses are constructed with the addition of “to be”.

1. Future perfect is basically perfect radical + future of to be (amav + erit => amaverit)
2. Pluperfect is perfect radical + imperfect of to be (amaverat)

Imperfect 2nd conjugation

About “je finissais”, the imperfect is always formed by adding “ais, ais, ait, ions, iez, aient” to the 1st person plural radical of the present form, so “nous FINISSons” ==> “je finissais, etc.”. The “s” is doubled to avoid sounding like a “z”, it is not an irregularity (or if you prefer, the writing is irregular so the pronunciation isn’t).

This said, you should have a look at finire. Pluperfect subjonctive looked like this : “finivíssem finivísses finivísset finivissémus finivissétis finivíssent”, and in French “que je finisse, que tu finisses, qu’il finisse, que nous finissions, que vous finissiez, qu’ils finissent”. Very similar, is it not?

Praeterit

The praeterit comes directly from Latin as well. Latin have more conjugations than French (5 vs 3), but to simplify it’s like Latin’s first conjugation (are) became French’s first (er), Latin’s “ire” verbs became French’s second, and the reste French’s third.

First conjugation

1. Amavi ====> j’aimai
2. Amavisti ===> tu aimas
3. Amavit ===> il aima (lost the ending t a long time ago too)
4. Amavimus => nous aimâmes
5. Amavistis => vous aimâtes
6. Amaverunt => ils aimèrent

=> mostly lost the “vi” part except first person.

Second conjugation

1. Finivi ====> je finis
2. Finivisti ===> tu finis
3. Finivit ===> il finit
4. Finivimus => nous finîmes
5. Finivistis => vous finîtes
6. Finiverunt => ils finirent

=> also lost the “vi” part. Finire is Latin’s forth conjugation.

Third conjugation

1. Potui ====> je pus
2. Potuisti ===> tu pus
3. Potuit ===> il put
4. Potuimus => nous pûmes
5. Potuistis => vous pûtes
6. Potuerunt => ils purent

=> lost the “ot” and “i” parts.
azeazeaze

1. Attendi =====> j’attendis
2. Attendisti ==> tu attendis
3. Attendit =====> il attendit
4. Attendimus ==> nous attendîmes
5. Attendistis => vous attendîtes
6. Attenderunt => ils attendirent

=> almost perfectly the same!