First, which type of FSA is it? A general health FSA or a limited-purpose FSA (like only for dental or vision)?
If you changed over to a general health FSA, then as of the month in which you were covered on the first day of the month by the FSA, you were no longer able to contribute to your HSA. However, your HSA doesn't go away and you can still pay for qualified medical expenses from it - you just can't contribute to it any longer.
You can start your FSA with your new job, by signing up and indicating how much you want to contribute (unless your employer is contributing) - your HR people will have the details. That fact that you previously had HDHP coverage and an HSA doesn't matter.
Note that you cannot reimburse yourself from your HSA for any expenses that were also covered (paid) by the FSA. You get one tax break or the other, but not both.
Also you need to go back and see how much you contributed to your HSA. Your annual HSA contribution amount is actually calculated month by month in your case, so you would take your full annual HSA contribution limit and multiple it by the ratio of the number of months you had HDHP coverage on the first of the month (and NO FSA coverage on the first of the month) divided by 12. So if your full annual HSA contribution limit would have $3,450 (2018) and you switched to the FSA on June 15th, then your actual HSA contribution limit would be $1,725 (because you would have had HDHP coverage for January through June).
If you find that you probably have already contributed more than that, then if you are doing your 2018 return, TurboTax will tell you that you made excess contributions. TurboTax will ask you if you will withdraw the excess by the due date of the return (I would assume that this is on extension, so October 15th). To do that, you must contact your HSA custodian and tell them that you want to withdraw an excess contribution (use this exact phrase) equal to the amount that TurboTax tells you in the HSA interview. Don't make this request until you know the exact number (i.e., don't guess). The excess will be added to Other Income, but that's OK because the custodian will send you a check for the excess.
If this is for 2019, then come back and tell me because I had to make some assumptions about your details.