So I took a level in sorcerer for a paladin and the DM picked out the assortment of cantrips and spells for me for story reasons. One of them is green-flame blade.

I can take 2 attack actions because of 5 levels in paladin, if I use green flame blade will I only be able to do the one attack action or can I use both with the cantrip active?

Casting a spell takes an action, so you use your Action to cast GFB which allows you to make one attack

thanks fam

Using the "Cast a Spell" action to use Green-Flame Blade will give you one GFB attack, no matter how many attacks you would normally be making using an Attack Action. Also note that other features that interact with "when you take the Attack Action" aren't going to trigger on the Cast a Spell action you use to cast GFB, although "when you make a melee weapon attack" features will. 

OP, I'm sensing you are under the effect of a common misconception: you do not have two "attack actions". You have a feature, Extra Attack, which allows you to make two weapon attacks when you take the Attack action. CC already mentioned some of this, and I would recommend you read this thread as we just had this conversation a little over a week ago. It'll clear up a lot for you.

It was more a case that I'm trying to understand everything the DM put on me. More or less I wanted to go one way and for story reason he went into an entirely different direction and I'm trying to make the best of my options.

Well, we're on our way to the depths of hell and the spells and cantrips I was given were Gust, GFB, thunderclap and a homebrew cantrip I made and DM authorized to give my paladin more range options and the spells given were sleep and featherfall.

I'm assuming it's related to the deity Nathair Sgiathatch that my paladin's deity called in for assistance (DM's choice, not mine), but the weapons I just got back from getting enchanted (and if I didn't put my foot down on waiting the 3 in game days I had left to do so I wouldn't have even gotten that after spending 1k gold to get them enchanted in the first place) do more damage in the 2 attacks I can take per action (total 2d6+10 thunder for 2 main attacks and 1d8 lightning for the two weapon fighting bonus action) and the spells I received for a trek through hell are so situational/ and/or useless that I'm likely to never use them in any serious capacity other than my home brew cantrip because it's actually useful for what I assume will be the main enemies for hell (essentially turns a single melee attack into a ranged attack 30/80 at the cost of a bonus action per normal attack)

Long and short. I wanted to go draconic origin with more appropriate and versatile spell options because me and another player in the campaign had so many similar plot points by accident we more or less started making each other's characters' backstories blend somewhat with DM's knowledge.

And then he chose wild magic and picked my sorcerer abilities for me 

The only reason I was looking for ranged options is that about 10 enemies or so we've fought in a row have had the capacity to fly. So I homebrewed the cantrip so I can still attack enemies that decided to fly out of dagger range.

And I say featherfall is situational is because in the 4 events where it would have been handy, 2 were acrobatics throws that I succeeded (I had +6 to acrobatics at the time, it's +7 now), one I forced out just to use it and the other was involving a party member falling and the DM ignored me saying that I was going to catch him from a 10 ft fall off a wall.  Gust is situational because in combat I am typically in enemy faces stabbing said face with a spear and we haven't been in a situation where gust has been any use since session 1, green flame blade does less than my attack actions and does even less because we're trekking into hell where most of everything is resistant to it and the last one I had to add in myself to balance out the longer distances.

Then as you said it, sleep is pointless to a place where nothing sleeps

His response was "the threat of wild magic is always looming" when I wasn't going for wild magic in the first place and I will likely never trigger the effect until the DM railroads me into using something that will trigger the roll

Quote from sfPanzer >>

Wow I'd hate to be in your position. Unless it's completely plot related the DM should have no say in how you build your character, that includes multiclassing, apart from banning specific things he in general doesn't want to have in his game. The reason he gave you is not even a proper reason.

 Absolutely agree with this and I've been playing and DM'ing D&D consistently every year since 1978. Even a warlock patron cannot select what spells a PC takes; a pact is an agreement, NOT a dictatorship. Your DM forcing you to play your character his way is utter egotistical nonsense. Even three years after the original post, I strongly recommend any player in this kind of situation find another DM. This kind of DM is not a friend or anyone to hang around with.

I agree with your statement "Agreements are not gifts, but rather contracts." My warlock's pact went as follows:

Sender of Ravens for Sorrowful Plights
This pact I pledge through this faithful rite.
In brightest day, in blackest night
No undead shall escape my sight.
Let those filled with a deathless spite
Beware your power and my Hexblade’s might.

As can be seen above, my warlock has a pact with the Raven Queen to hunt down undead where ever they may be. But he's also a paladin who swore to Silvanus the following Oath of Vengeance:

Vengeance I shall be;
For Thee, Silvanus, for Thee;
Power hath descended forth from Thy hand;
That my Self may swiftly carry out Thy command
To strike down threats to the Wild with great vengeance and fury enfiled;
And a red river forth I shall flow to Thee;
Teeming with despoilers’ souls shall it ever be.

So when my DM threw my paladin/warlock into the Strahd campaign and had minions of Strahd start trashing the forests, everything I had planned for my character went straight into the garbage can. Not because the DM dictated what my character would do but because the character backstory and build I came up with demanded my character either remain true to his oath and pact or he could ignore the situation, become a fallen paladin and have the Raven Queen really angry with him at the same time he was in an area known for undead and raven lycanthropes. The decision was completely up to me. But playing a fallen paladin with warlock abilities he would keep but not improve or change was also intriguing. So whichever I chose was going to be both entertaining and challenging.

And that is what defines a good DM .

Not tryin to tell you how to live your life but it kinda just sounds like you need a new DM. The whole point D&D is for it to be an interactive role playing game for everyone at the table, not so you can be told what to do and how to do it.