Just like in English with although and even if, you can express concession in French with two different expressions : bien que and même si.
BUT these two expressions won't be followed by the same tense mood.
Bien que + Le Subjonctif
To say although in French, we use the expression bien que followed by a verb in Le Subjonctif.
ATTENTION:
Do not confuse bien que (although) with expressions using bien followed by que (that):
J'aimerais bien que tu fasses le petit-déjeuner.
I would like you to make breakfast.
-> Here it's the expression aimer bien (to like) followed by que.
Même si + L'Indicatif
Même s'il n'est pas fatigué, il devrait aller se coucher.Even if he is not tired, he should go to bed.
Même si l'on ne s'entend pas, c'est quand même mon frère! Even if we don't get along, he's still my brother!
Même si means even if / even though, however it's always followed by a tense in L'Indicatif and never Le Subjonctif.
The difference between bien que + Le Subjonctif and même si + L'Indicatif is similar to the difference between although and even if, the first being more elegant and subtle than the latter.
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Examples and resources
Même s'il n'est pas fatigué, il devrait aller se coucher.Even if he is not tired, he should go to bed.
Même si l'on ne s'entend pas, c'est quand même mon frère! Even if we don't get along, he's still my brother!
Bien qu'il ne soit pas fatigué, il devrait aller se coucher.Even though he is not tired, he should go to bed.
Même si elle lui parlait, il ne changerait pas d'avis.Even if she spoke to him, he wouldn't change his mind.