我最后的生日（我去年的生日）*last year=去年（qu4nian2)

我跟我家总是一起庆祝我的生日。

（我总是跟我的家人一起庆祝生日。* ”Family“ can be translated into "家人“ in this context.）
但是第一次我的最后的生日是我跟她们不在时。

(但是，去年过生日的那天，我第一次没有跟她们在一起。）
(我在Montpellier学习，她们住在Narbonne。)

(我在蒙彼利埃学习，而她们住在纳博讷。）蒙彼利埃：Meng2bi3li4ai1; 纳博讷：Na4bo2ne4

*”而“ means "but” here.)
在(?)生日，我有很多课。下午八点一刻放学。

(在去年我过生日的那天，我有很多课。晚上八点一刻放学。）
所以打早下了课。差不多下午六点半放学。

（那天是我的生日，我差不多六点半就回家了。）
因为要赶火车，就得缺了一课。（我缺了一节课。）
到我的家，妈妈已经给我买了蛋糕。

（到家以后，我看见妈妈已经给我买了蛋糕。）
我跟我妈妈和（还有）妹妹一起吃了蛋糕，（+觉得）很高兴。
以后（然后），她们送给我一封信。
我看这封信地流泪了。很感人了。

（我看信的时候流泪了。那封信很感人。）

Notes :

最后的生日 => is it right ? Because I meant my last year's birthday (the most recent one today)

And what I wanted to say (roughly) :

I've always been spending my birthday with my family.
But for the first time, my birthday happened to be when I wasn't with them.
(I study in Montpellier and they live in Narbonne.)
On my birthday, I had many classes. I was finishing school at 8:15 pm.
So I left school earlier, around 6:30 pm.
I missed one class because I had to catch up the train.
When reached home, my mom already bought me a (birthday) cake.
I was really happy to eat it with my mom and little sister.
Afterward, they gave me a letter.
I cried reading it, it was really touching.

Thank you in advance for correcting my Mandarin ! (and sorry for all the mistakes)

Hello, Aurore

I was really happy to read that you celebrated your birthday with your family last year, although you were in different cities at that time. Some corrections I made are different from your original post. Hope you will find them useful.

Yang

我最后上次的生日

我跟我家总是跟我家人一起庆祝我的生日。
但是第一次我的最后我上一次的生日是时我跟她们不在时不在他们身边。
(我在Montpellier学习，她们住在Narbonne。)
在(?)我生日那天，我有很多课。下午八点一刻放学。
所以打早提前下了课。差不多下午六点半放学离开。
因为要赶火车，就得不得不缺了一课。
到我的家时，妈妈已经给我买了蛋糕。
我跟我妈妈和妹妹一起吃了蛋糕很高兴。
以之后，她们送寄给我一封信。 ,
我看这封信地流泪了。信很感人了。

Notes :

最后的生日 => is it right ? Because I meant my last year's birthday (the most recent one today) 

Non, ce n'est pas correct. Parce que cette phrase veut plutôt dire, le dernier anniversaire dans la vie. Donc la personne dont on parle est déjà morte.

And what I wanted to say (roughly) :

I've always been spending my birthday with my family.
But for the first time, my birthday happened to be when I wasn't with them.
(I study in Montpellier and they live in Narbonne.)
On my birthday, I had many classes. I was finishing school at 8:15 pm.
So I left school earlier, around 6:30 pm.
I missed one class because I had to catch up the train.
When reached home, my mom already bought me a (birthday) cake.
I was really happy to eat it with my mom and little sister.
Afterward, they gave me a letter.
I cried reading it, it was really touching.

Thank you in advance for correcting my Mandarin ! (and sorry for all the mistakes)

我最后的生日（一定不能这么写，我的生日）

我跟我家总是一起庆祝我的生日。 我总是跟我的家人一起过我的生日。
但是第一次我的最后的生日是我跟她们不在时。 但是第一次，我生日时我跟他们不在一起。

(我在Montpellier学习，她们住在Narbonne。) （我在..学习，他们住在..）
在(?)生日，我有很多课。下午八点一刻放学。 生日那天，我有很多课，下午8:15才能放学。
所以打早下了课。差不多下午六点半放学。 所以我提前离开了，大约下午6:30的时候。
因为要赶火车，就得缺了一课。 我因为要赶火车缺了一堂课。
到我的家，妈妈已经给我买了蛋糕。 到家时，妈妈已经给我买了蛋糕。
我跟我妈妈和妹妹一起吃了蛋糕很高兴。 我很高兴，跟妈妈和妹妹一起吃了蛋糕。
以后，她们送给我一封信。 之后，她们送给我一封信。
我看这封信地流泪了。很感人了。 我边看边哭，信写得非常感人。

Notes :

最后的生日 => is it right ? Because I meant my last year's birthday (the most recent one today)

And what I wanted to say (roughly) :

I've always been spending my birthday with my family.
But for the first time, my birthday happened to be when I wasn't with them.
(I study in Montpellier and they live in Narbonne.)
On my birthday, I had many classes. I was finishing school at 8:15 pm.
So I left school earlier, around 6:30 pm.
I missed one class because I had to catch up the train.
When reached home, my mom already bought me a (birthday) cake.
I was really happy to eat it with my mom and little sister.
Afterward, they gave me a letter.
I cried reading it, it was really touching.

Thank you in advance for correcting my Mandarin ! (and sorry for all the mistakes)

我上次的生日

我跟我家人总是一起庆祝生日。
但是我上次生日刚好她们不在。
(我在Montpellier学习，她们住在Narbonne。)
生日那天，我有很多课。我晚上八点十五分放学。
我因为要赶火车，所以晚上六点半提早离开学校。因此就缺了一堂课。
回到家，妈妈已经给我买了蛋糕。
我跟妈妈和妹妹一起高兴的吃蛋糕
之后，她们送给我很感人的一封信。
我看这封信就流泪了。

Notes :

最后的生日 => is it right ? Because I meant my last year's birthday (the most recent one today)

And what I wanted to say (roughly) :

I've always been spending my birthday with my family.
But for the first time, my birthday happened to be when I wasn't with them.
(I study in Montpellier and they live in Narbonne.)
On my birthday, I had many classes. I was finishing school at 8:15 pm.
So I left school earlier, around 6:30 pm.
I missed one class because I had to catch up the train.
When reached home, my mom already bought me a (birthday) cake.
I was really happy to eat it with my mom and little sister.
Afterward, they gave me a letter.
I cried reading it, it was really touching.

Thank you in advance for correcting my Mandarin ! (and sorry for all the mistakes)