Although some secondary sources (e.g., files at WorldConnect) show these parents for our subject:
Father:  Pero Dias CARRICO
Mother:  Isabel LIMA
there is no proof of the connection.

Many secondary sources give Peter's birthplace as France (or Normandy, France).  There is no indication whatsoever of Peter's birthplace in any primary record, so the "French connection" is pure myth.  Orthographically, the name appears most likely to be Portuguese, but phonetically similar surnames are Spanish (CARRICA, CARACO) or Italian (CARICO, CARACO).  Any of these origins would be consistent with our subject's DNA haplogroup subclade (see Figure 2, Map E, for current distribution of J2a1b).

1a.  Charles County, Maryland.  Patent Book 18, p. 80 (online in the Archives of the CARRICO-L mailing list at RootsWeb.com):

15 June 1674 Came Samuel Dobson of Charles County and proved his right to six hundred and fifty acres of land for transporting John Daniels, Roger Roberts, Thomas Thompson, John Tibbot, Alexander Seasor(?), Samuel Lee, Henry Keeling, Ralph Givin(?), William Marsh, George Sutton, John Dorrinton, Peter Curricoe, and Mary Cooke into this province to inhabit.

17 June 1674 Warrant then granted to said Samuel Dobson for six hundred and fifty acres for transporting the thirteen above mentioned persons into this providence to inhabit in Anno 1674. Certified the 17th of September 1674.

It has been assumed that Peter was an adult when he was transported, but I'm not certain that assumption can be made.  Peter was granted 50 acres of land in 1681, the standard grant after serving out a service contract, so I think we can be certain he was an adult at that time.  It's unlikely that he married while still indentured, so it's probably safe to assume he married in or after 1681.

1b.  Linda Boorom, transcriber.  Peter Curricoe Transported 1674.  Linda Boorom's transcription of the above record.

2a.  Linda Boorom, transcriber.  Charles Co. Court 1696. 

2b.  Linda Boorom, transcriber.  Peter Carrico Levy Free 1719 & 1720. 

3.  Robert W. Barnes.  1992.  "Charles County Depositions, A-G."  Maryland Genealogical Society Bulletin, v. 33, n. 4, pp. 693-711.  On p. 699:

CARRICOE, James, age 70, 28 Sept. 1763, stated his father was Peter Carricoe; CHLR P#3, 59:614.

4.  According to a post by Carol Mitchell to the CARRICO-L mailing list (Archives online at RootsWeb.com; search on carolmit@usaor.net to find her posts):

Peter was granted 50 acres in MD in 1681.

Peter sold 60 acres to Walter Story on 9 Mar 1707, Charles Co., MD.  No wife waived dower.

In 1719, Peter requested to be excused from taxation (in Charles Co., MD) due to old age.

Sadly, Ms. Mitchell is now deceased, and no one so far seems to have located her papers.  All of her research may be lost to us.

5.  Homer E. Carrico.  1951.  "The Carrico Family." Filson Club Historical Quarterly 25:  217-252 (1981, Genealogical Publ. Co., Baltimore, MD, pp. 215-250 — caution, Homer's article is rife with errors).  On p. 215:

A tradition, stoutly asserted by some Carrico descendants, is that an earlier Peter Carrico, father of Peter and Abel, came to the Colonies under the auspices of the second Lord Baltimore.

Saying that Peter came to the Colonies "under the auspices" of Lord Baltimore is a bit of snobbery.  The earlier Peter, who did exist, arrived in Maryland as an indentured servant, which would have placed him socially so far beneath Lord Baltimore that Peter would have been unknown to him.

6.  Messages in the Carrico Family Genealogy Forum (online at GenForum.com):  see especially:  "CARRICO origins 1674."

7.  Messages in the Portugal Genealogy Forum (online at GenForum.com):  see especially:  "CARRICO--England to America 17th Century."

8.  Descendants of Peter Carricoe I by Al Beard.

9.  CARICO, CARRICO, and CARRICOE Families by Linda Boorom.

10.  WorldConnect / Ancestry World Trees (online at RootsWeb.com/Ancestry.com).

Webster's New Geographical Dictionary.  (1977. G. & C. Meriam Co. Publ., Springfield, MA).  On p. 1048:

Saint Marys City or formerly Saint Marys.  Village, Saint Marys co., S Maryland... first settlement in Maryland made here Mar. 1634 by Leonard Calvert, arriving in the ships Ark and Dove; site purchased from the Indians; prospered as capital of Maryland until 1694; later declined rapidly until few traces of town remained; revived 1934 at Tercentenary Celebration and site now maintained by state of Maryland.