The first sentence is wrong, it's not correct at all. You can say "je suis content que tu aies trouvé", yep, but "que j'ai trouvé" nope.
Pour "je" it's infinitive, here is your rule. Je suis triste d'avoir perdu. J'aimerais aller au cinéma / j'aimerais que vous alliez au cinéma, it's the same rule.
It's logical i guess, you dont have to repeat "je" twice if u are talking about you.