Can I get 350 Euro from an ATM in Paris or are the amounts more "standard" such as 50, 100, 200 etc? The reason I want 350 is it's the closest amount of Euro's to my daily maximum withdrawl amount in dollars at my bank.

From my experience, there is an "Other Amount" button you can push. Otherwise, yes, the amounts are pretty standard.

I'm pretty sure I was able to withdraw 350E from a BNP Paribas ATM in Paris.

get your bank to lift the limit in consideration of the conversion

You can take out in multiples of either €10 or €20 depending on the machine. Some machines will have a lower per transaction limit. Often €250, but you can keep withdrawing from the same or other ATMs up to your daily limit.

You can also get your own bank to raise your daily limit.

I'm in Paris right now and was able to withdraw 600 euros in one transaction at a BNP Paribas ATM. I called my bank to raise the withdrawal limit.

I have visited a few ATMs that had only increments of €20. Had I wanted €250, I would have needed to ask for either 240 or 260.

It all depends on whose ATM it is.

Some banks will not allow you to go over a certain daily amount even on request.

In my case with Fidelity's cash card, I can go inside the bank and get over $1,500 in local currency, but outside at the ATM there is a lower limit. (Don;t recall the exact amount; something like $500.)

Yes you can withdraw 350 euro and they give you your cash in all denominations.